Maya's Text Book Pages

Questions 3, 7, and 11. Pages 110 - 111


3. Walter walks across a rectangular field in a diagonal line. Maria walks around two sides of the field. They meet at the opposite corner.


7. What is the height of the wheelchair ramp? Give your answer to the nearest tenth of a centimetre.

The answer is 12.6

11. Johan has a 300cm ladder that he leans up against a wall. The safety sticker on the side of the ladder shows that the bottom must be placed between 70 cm and 110 cm away from the wall. What are the minimum distance and maximum distance up the wall that the ladder can reach? Give your answers to the nearest tenth of a centimetre.

The answer is 291.7 cm.


Here are two videos that may help you.







Here's a link to also help you.

Louis' Homework book: 30 questions 2, 3, 4

Homework Book Pages 30 questions 2, 3, 4

2) Use the relationship to determine the length of C in each triangle, to the the nearest whole number. Show your work.

A)

b2=c2 - a2

b2=262 - 242

b2=676 - 576

b2=100m2

square root 100 m2 and it becomes 10m

B)

a2=c2 - b2

a2=392 - 152

a2=1521 - 225

a2=1296 cm2

square root 1296 cm2 and it becomes 36cm

3) Determine the length of each hypotenuse. Show your work.

A)

a2 + b2 = c2

402 + 92 = c2

1600 + 81 = c2

1681 cm2 = c2

square root 1681 cm2 and it becomes 41cm

B)

a2 + b2 = c2

352 + 122 = c2

1225 + 144

1369m2 = c2

square root 1369 m2 and it becomes 37m

4) What is the length of each hypotenuse, to the nearest centimeter? Show your work.

A)

a2 + b2 = c2

82 + 92 = c2

64 + 81 = c2

145 = c2

square root 145 cm2 and it becomes 12.04cm

B)

a2 + b2 = c2

102 + 62 = c2

100 + 36 = c2

136 cm2 = c2

square root 136 cm2 and it becomes 11.66 cm

Jennily's Textbook Pages

Pg 108-110

Question 3,9,11

3. Walter walks across a rectangular field in a diagonal line. Maria walks around two sides of the field. They meet at the opposite corner. Express your answer to the nearest metre.

A) How far did Maria walk?

B) How far did Walter walk?

C) Who walked further? By how much?

A) Maria walked 420 Km.

B) Walter walked 323 Km.

C) Maria had walked more further by 97m.

9. A checkerboard is made of 64 small squares that each have a dimension of 3cm * 3cm. The 64 small squares are arranged in eight rows of eight.

A) What is the length of th diagonal of small square? Give your answer to the nearest tenth of a centimetre.

B) What is the total length of the diagonal of the board? Give your answer to the nearedt centimetre.

A) a square + b square = c square

3 square + 3 square = c square

9+9=18

c square = 18

c = 4.2 cm square

B) 32cm

11. Johan has a 300-cm ladder that he leans up against a wall. The safety sticker on the side of the ladder shows that the bottom must be placed between 70 cm and 110 cm away from the wall. What are the minimum distance and maximum distance up the wall that the ladder can reach? Give your answers to the nearest tenth of a centimetre.

The maximum is 291.7 cm, and the minimum is 279 cm.

Meldrick's Textbook Pages

The pages I had to do 7, 10, 13, and the deadly question 16.

Number 7

What is the missing length of the leg for each triangle? Give your answer to the nearest tenth of a millimetre.

a)

a²+b²=c²

a²+5²=9²

a²+(5x5)=(9x9)

a²+25-25=81-25

a²=56 mm²
√a²=√56 mm²

a=7.5 mm

b)

a²+b²=c²

a²+11²=15²

a²+(11x11)=(15x15)

a²+121-121=225-121

a²=104 mm²

√a²=√104

a=10.2 mm

Number 10

What is the minimum distance the player at third base has to throw to get the runner out at first base? Express your answer to the nearest tenth of a metre.

a²+b²=c²

27²+27²=c²

(27x27)+(27x27)=c²

729m²+729m²=c²

1458m²=c²

√1458=√c²

38.2m=c

The player must throw a distance of 38.2 metres.

Number 13

Determine the length of the base of the large triangle. Express your answer to the nearest tenth of a millimetre.

a²+b²=c²
8²+b²=10²

(8x8)+b²=(10x10)
64-64+b²=100-64

b²=36mm²

√b²=√36

b=6mm

b(2)=6(2)

Base=12cm

Number 16

The deadly number 16. Hopefully you won't need this guide, as it is for people who have been reduced to tears (not literally) by this question. But if you are one of these people, you are welcome to look at the answer.

What is the length of the red diagonal in the box? Express your answer to the nearest tenth of a millimetre.

Now, imagine that the triangle has been cut in half, from the top right corner to the bottom left corner, so that the diagonal is on a 'flat surface'. Using the height (5mm) and length (12mm), we can find the hypotenuse of the 'triangle' that was created when the rectangle was cut in half, using the Pythagorean theorem (height-a, length-b):

a²+b²=c²

5²+12²=c²

(5x5)+(12x12)=c²

25+144=c²

169cm²=c²

√169=√c²

13mm=c
After that, imagine turning the triangle so that you can see the red diagonal cutting a rectangle in half. You have already found the bottom of the rectangle (13mm), and you have the measurements for the right side of the rectangle, the width (7mm). Using the Pythagorean theorem, you can now find the red diagonal (width-a, bottom-b).

a²+b²=c²

7²+13²=c²

(7x7)+(13x13)=c²

49+169=c²

218cm²=c²

√218=√c²

14.8cm=c

Hopefully, you found that helpful. Good night (it's 1:05 AM), and goodbye.

Mussie Mesgun Homework Book: Even Questions

2) Use the relationship to determine the length of C in each triangle, to the nearest whole number.show your work.

A) a²+c²=b²
24² cm 26² cm=c²

-576 cm + 676 cm=c²

100 cm=c²

√100 cm=√c²

10cm=c

B) a²+c²=b²

39² +15²=c²

1521 + 225 =c²

√1746=√c²

41.78 =c

42 = c

4)What is the length of each hypotenuse, to the nearest centimetre? show your work

A) a²+b ²=c²

8² cm + 9² cm=c²

64 cm +81cm=c²

√145cm =√c²

12.0cm=c

B) a²+b²=c²

6² cm +10² cm=c²

36 cm+100 cm=c²

√136cm²=√c²

11.6 = c
12 = c

6) Find the height of triangle with a base of 4 cm and a hypotenuse of 11 cm. Round to the nearest tenth of a centimetre. show your work

a²+b²=c²

-4² cm +11² cm=b²

-16 cm +121cm=b²

√105cm=√b²

b=10.2
b = 10 cm

8) Ellie and Lucas are going to the skateboard park to try out the new ramp.

A) is the new ramp a right triangle? explain your thinking

Yes is a right triangle because it as a 90' angle

Joshua's Pythagoras Scribe Post

6. Determine the length of the leg for each right triangle.

9. Tina wants to construct a path along the diagonal of her yard. What length will the path be? Express your answer to the nearest tenth of a metre.

12. The hypotenuse of the triangle cuts the circle in half. What is the diameter of the circle? Express your answer to the nearest tenth of a centimetre.

15. The coordinate grid shown was drawn on centimetre grid paper. What is the line segment of AB? Express your answer to the nearest tenth of a centimetre.

Here is a video to help you:

Here is a link to help you.

If I made any mistakes, please tell me!

Ana Lopena's Pythagoras Scribe Post

12. While shopping online, Jin Hun finds a square rug with an area of 11m2. He needs to know if it will fit in his 4m x 5m bedroom.

a) Estimate the side length of the rug to one decimal place.

b) Check your estimate with a calculator.

c) Will the rug fit? Explain.

Yes, because the side length of the room is 4m and 5m and the side length of the rug is 3.3m.

13. Stella is planning an outdoor wedding. She would like a square dance floor with an area of 115m2.

a) Determine the side length of the nearest tenth of a metre.

b) Stella finds out that the dance floor will be made up of 1m2. What are the two side lengths the dance floor can have that are the closest to what she wants?

10m x 10m or 11m x 11m

c)What are the two square areas for the dance floor that Stella can choose from?

100m2 or 121m2

d) Which area will Stella choose? Explain.

I think that Stella will choose 121m2 because it is closer to the area that she wanted.

John's Pythagoras Scribe Post

Textbook Pages 98-100

#1 and 17

1.Explain how to estimate √28 to one decimal place without using a calculator.compare your answer with a classmate's

Answer:

To estimate √28 you have to find the two closest perfect squares. 25 and 36 are just right because 28 is between these two perfect squares. There are two method or ways to find the estimate of the square root of 28

The first one is a number line

HOW?

What I did was put the perfect squares on both ends of the number line and then I decided which is closest 28 which was 25 and I took a guesstimate and I got 5.3

Other way is this

HOW!?

The method is the same as the number line except you write it different. You just find what number 28 is closest to which is 25 and take a guesstimate that would be logical not over 5.5 since its closest to 25.

18.

a) Evaluate √9.

b) Estimate the square root of your answer

in part a), to one decimal place.

c) Use a calculator to check your estimate.

Express your answer to the nearest

hundredth.

d) How close is your estimate in part b)

to your calculation in part c)?

A)How to find the square root of 9? 9 is a perfect square so its easy, what I did was I looked for other perfect squares that are closest to 9 like 4 and 16 so 4 is 2x2 and 16 is 4x4 so 9 is 3x3 since its in the middle of 2 and 4

B)

C) The calculation is 1.73

D)My estimation in Part b was 0.2 larger than the actual calculation.

(HEY GUYS IF YOU FIND ANY MISTAKE, LEAVE A COMMENT AND PUT THE RIGHT ANSWER)

Christian T's Pythagoras Scribe Post

14. Alex is thinking of a number. The number has a square root between 7 and 8 and is divisible by 12.

a) What number could he be thinking of?

b)Is there more than one answer? Explain.





19. Estimate √160 100. Explain how you determined your estimation.

Here is a video to help you out.


Here's a link to help you. http://www.homeschoolmath.net/teaching/square-root-algorithm.php

Jasmin's Pythagoras Scribe Post

Textbook Pg.98-100
















A) 16 is a perfect square that is smaller than 20.
25 is a perfect square that is greater than 20.











B) (I measured 4cm)












Question 15:
Order the following numbers from least to greatest :

My answer:

Here is a link about square roots.
Here is a video on square roots.


** Please tell me if I did anything wrong, I'll try to fix it!

Jennily's Pythagoras Scribe Post

Question 1,6,13,20

1.) Describe using words and symbols the relationship among the areas of the three squares shown.

The relationship is the S2 + V2 = T2 is the same as A2 + B2 = C2.



6.) Write an addition statement using the areas of these three squares.
The addition statement That was shown was 25 + 144 = 169

B) What is the length side of each square?
25 = 5
144 = 12
169 = 13

C) Describe using words and symbols, the relationship between the side length of each square.
The addition of the two smaller squares are equal to the largest square.

13.) A small triangular flower bed has a square steeping stone on each side, is the flower bed the shape of a right triangle ? Explain.
No it isn't because the two smaller square isn't equal to the largest square. 4800+4800=9600

20.) A right triangle has sides of 13 cm, 4 cm, and 5 cm. Attached to each side is a semi circle instead of a square. Describe the relationship between the areas and the semi circles.
The area of the two smaller semi circle is equal to the area of the square by the hypotenuse.

There is my post hope you like it and if I made any mistake please tell me.
I found a Pythagoras trivia game here is the site hope you have fun.
http://www.funtrivia.com/playquiz/quiz2049161776b68.html

Joshua's Pythagoras Scribe Post

4. What are the areas of the three squares shown?

9. a) Calculate the areas of the three squares
b) Is this a right triangle? Explain.

12. Use the Pythagorean relationship to find the unknown area of each square.

17. What is the area of the square that can be drawn on side c of each triangle?

Here is a video to help you out:


For more help check out this link.

If I did anything wrong, please tell me!

Christian Andulan's Pythagoras Scribe Post

Lets start things off with our homework ! Pages 91-94, all questions.

*Sorry for the messy work
I had to do questions 2, 7, 14 and 18.

2.) A triangle has side lengths of 7cm, 11cm, & 15cm. Explain how you can determine whether it or not it is a right triangle.

" a² + b² doesn't equal to c². This isn't a right triangle "

7.The sides of a right triangle measure 9cm,12cm and 15cm.

a)What is the area of each square attached to three sides of the right triangle?

b)Write an addition statement showing the relationship between the areas of the three squares.

14.) Show whether each triangle in the table is a right triangle.

18. The diagram is made of two triangles and five squares.

a) What is the area of square x?

b) I did not understand this question.

Katerina's Scribe post

Questions 1 , 6 , 13 and 20.

1.) Describe using words and symbols the relationship among the areas of the three squares shown.

The relationship is the S2 + V2 = T2 is the same as A2 + B2 = C2.

6.) Write an addition statement using the areas of these three squares.

The addition statement I got was 25 + 144 = 169

B.) What is the side length of each square?

25 = 5x5 = 52

144 = 12x12 = 12 2

169 = 13x13 = 132

5 cm

12 cm

13 cm

6.) Describe using words and symbols the relationship between the side lengths of the squares.

The relationship between them is that the sum of the areas smaller squares equal the areas of the largest square.

13.) A small triangular flower bed has a square steeping stone on each side, is the flower bed the shape of a right triangle ? Explain.

No it isn't because the sum of the smaller squares isn't equal to the area of the larger square.

20.) A right triangle has sides of 13 cm, 4 cm, and 5 cm. Attached to each side is a semi circle instead of a square. Describe the relationship between the areas and the semi circles.

The sum of the area of the two smaller semi circles is equal to the area of the squares by the hypotenuse.

Here is a Pythagoras game that you can try.

Here is a site to help you understand this.

If I made any mistakes please let me know!

Angelique's Pythagoras scribe post

This is my scribe post on questions 5, 10, 15, and 19.

You can practice figuring out the unknown side for the right triangle here.

If you don't want to practice and just learn more you can go to this site.

Here is a video to help understand more about Pythagoras.
Skip to 0:35 if you don't want to wait.

If I had any mistakes or you don't understand something please tell me so I can fix them.