*PYTHAGOREAN RELATIONSHIP"*is the relationship between the LENGTHS of a right triangle. To know that the right triangle has a correct sides, you need to see if the two legs are equal to the hypotenuse.

This is a place for the community of learners in Room 8-16 to learn and enjoy math. It is an extension of the classroom making it accessible 24 hours a day, 7 days a week.

## Monday, February 27, 2012

### Jandrenn's PYTHAGOREAN REALTIONSHIP

## Tuesday, February 14, 2012

### cheleseb pythagorous post

A+B=C

that method is the way you find out if the triangle is a right triangle. you take the a + b-c and fill the numbers in.

if the to legs add up to the hypotenuse then you have a right triangle.

2. answer this missing side.

one leg equals = 12 which is A side

the other = 5

so we go c=a+b

c2=12+5

c2= (12x12) + (5x5)

c2= 144+25

c2=169( sqaure root it )

c=13

so the answer will be the c= 13 2

3.is the triangle a right triangle? prove it !!!

well one side equals 8 the other equals 6 so

a2+b2=c2

8+6=14

14 2=11 2

there for the triangle is not a right triangle.

### Mil's Pythagoras Scribe Post

**pythagorean relationship is a relationship between the LENGTHS of a right triangle. To know that the triangle has a correct sides, you need to see if the two legs areequal to hypotenuse.**

### pathagorous post

A+B=C

that method is the way you find out if the triangle is a right triangle. you take the a + b-c and fill the numbers in.

if the to legs add up to the hyptenuse then you have a right triangle.

2. answer this missing side.

one leg equals = 12 which is A side

the other = 5

so we go c=a+b

c=12+5

c= (12x12) + (5x5)

c= 144+25

c=169( sqaure root it )

c=13

3.is the triangle a right triangle? prove it !!!

well one side equals 8 the other equals 6 so

a+b=c

8+6=14

14=11

there for the triangle is not a right triangle.

### Michael's Pythagorean Relatiohnship

Answer:

c2 is equals to a2 + b2.

a2 + b2 = c2

52 + 122 = c2

25 cm2 + 144 cm2 = c2

169 cm2

13 cm2

a2 + b2 = c2

62 + 82 = 112

36 + 64 = 121

100 = 121

NOT A RIGHT TRIANGLE

### Anmarie's pythagorean relationship post

The Pythagorean Relationship can be used to show if a triangle is a right triangle.

Left side:

6 squared+8 square= 10 squared

(6x6)+(8x8)=(10x10)

36+64=100

C squared= a squared+b squared

C squared= 12 squared+5 squared

C squared=(12x12)+(5x5)

C squared=144+100

C squared=244 squared

square root of "C" squared= square root of 244 is 15

C square= 15cm

8 squared+6 squared=11 squared

(8x8)+(6x6)=(11x11)

64+36=121

square root of "C"squared= square root of 121cm squared is 11

C=11cm

the triangle a right triangle.

## Monday, February 13, 2012

### Amiel's Pythagoras Post 4, 5, 10

e=30mm

e= 30

*²*

e=30x30

e=900mm

e=30x30

e=900mm

*²*

f=40mm

f=40

*²*

f=40x40

f=1600mm

*²*

g=50mm

g=50

*²*

g=50x50

g=2500mm

*²*

5. A right triangle has side length of 40mm, 75mm, and 85mm.

a) Sketch the right triangle and draw squares around each side of the triangle.

b) What are the areas of the three squares?

A=40mm B=75mm C=80mm

A=40

*² B=75*

*²*

*C=80*

*²*

*A=40x40 B=75x75 C=80x80*

A=1600mm B=5625 C=7225

A=1600mm B=5625 C=7225

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

A

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

A

*²*

*+B*

*²*

*=C*

*²*

1600+5625=7225

10. A triangle has the side lengths of 120mm, 160mm, and

1600+5625=7225

10. A triangle has the side lengths of 120mm, 160mm, and

*200mm. Is the triangle a right triangle? Explaing your reasoning.*

a+b=c

120+160= 280

280≠200

It is not the a right triangle because the leg of the triangle did not equal the hypotenuse.

### Ashlie's Textbook Questions

**12. While shopping online, Ji Hun finds a square rug with the area of 11m squared he needs to know if it will fit his 4m x 5m bedroom.**

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

**sqrt 9 sqrt 11 sqrt 16**

**|-------|-----------------------|-----------------------------|**

**3 3.31 4**

**b) Check with a calculator.**

**sqrt 11 = 3.316**

**c) Does the rug fit? Explain.**

**Yes, because the room is 20m and the rug is 11m.**

**__________________________**

**| _________|____4m___ |**

**|**

**| | |**

**| | | |**

**| = 4m x 5m = 20m2 = |**

**| | | 5m |**

**| | | |**

**| |_________|_________ | |**

**|__________________________|**

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

**a) What could he be thinking of?**

**sqrt 49 sqrt 60 sqrt 64**

**|-------------------------|---------------|----------|**

**7 7.74 8**

**b) Is there more than one answer?**

**No, 60 is the only number between square root that is a multiple of 12.**

**17. Carmen wants to mount 18cm x 18cm square board that is 4 times the area of the picture.**

**a) What is the area?**

**____________|_18cm________**

**| |**

**|**

**| 18cm**

**| |**

**= 18 x 18 = 324cm2 =**

**| |**

**| |**

**| |**

**|__________________________|**

**|**

**b) What is the**

**area of the board?**

**____________|____324cm_____**

**| |**

**|**

**|**

**| | 324cm**

**= 324 x 324 = 104.9 =**

**| |**

**| |**

**| |**

**|__________________________|**

**|**

**c) What are the dimensions of the board?**

**sqrt 324 = 18cm****____________|___18cm______****| |****|****|****| | 18cm****= =****| |****| |****| |****|__________________________|****|**### Ashlie's Pythagorean Relationship Post

*The pythagorean relationship is used for solving problems for finding the hypotenuse with 2 given legs. Also to figure out if the triangle is a right triangle or not.***1. Find The Missing Side Length.**

**c2 = a2 + b2**

**c2 = 52 + 122**

**c2 = (5x5) + (12x12)**

**c = 25cm2 + 144cm2**

**c = 169cm2**

**square root of 169 = 13cm**

**c = 13cm**

**2. Is This A Right Triangle? Show Your Work.**

**a2 + b2 = c2**

**62 + 82 = 112**

**(6x6) + (8x8) = (11x11)**

**36 + 64 = 121**

**100 /= 121**

*Not a perfect square because the legs don't make/equal the hypotenuse.*### mikyL's pathagorous scribe post

first of all:

we learned about the system its self.

hypotenuse- the right triangles largest slide in between the legs. the hypotenuse can be calculated many different ways as i will explain in ferther explanations.

yellow: 7cm

blue 4cm

purple:?

pathegrous- if you look to the left this is a pathagorous question.

to calculate it you need to know how much the sqaures are each worth. so we know that

*yellow is worth 7cm*and blue is worth 4cm. so nopw we know that A(sq.) + B(sq.) = C(sq.)

so to calculate that you do A+B+C

4+7=11cm (sq.)

now not always you will have a triangle that is a right triangle. if it is not a right triangle you must state that it isnt and say why. for example if the triangle does not have a little square in the middle of the legs, then it may not add up equal and it will NOT be a right triangle. :)

i hope you like my pathagourus post. I DONT HAVE ALOT OF INFORMATION BUT IF YOU HAVE ANY COMMENTS THEN POST THEM BELLOW AND I WILL TRY AND ANSWER THEM TO MY BEST ABILITIES :) THANKS!

### Pythagoras post

a)

c squared = a squared + b squared

c squared = 12 squared + 16 squared

c squared = (12 x 12) + (16 x 16)

c squared = 144 + 256

c squared = 400 cm squared

Then squared root "c" squared and square root 400 cm squared

c = 20 cm

b)

r squared = p squared + q squared

r squared = 16 squared + 30 squared

r squared = (16 x 16) + (30 x 30)

r squared = 256 + 900

r squared = 1156 m squared

Then square root "r" squared and then squared root 1156 m squared

r = 34 m

4. What is the length of each hypotenuse? Give your answer to the nearest tenth of a centimeter.

a)

z squared = x squared + y squared

z squared = 6 squared + 7 squared

z squared = (6 x 6) + (7 x 7)

z squared = 36 + 49

z squared = 85 cm squared

Then square root "z" squared and then square root 85 cm squared.

z = 9.21 cm

b)

d squared = b squared + c squared

d squared = 8 squared + 11 squared

d squared = (8 x 8) + (11 x 11)

d squared = 64 + 121

d squared = 185 cm squared

Then square root "d" squared and then square root 185 cm squared

d = 13.6 cm

5.

a) What is the area of each square attached?

a squared = 6 squared

a squared = 6 x 6

a squared = 36 cm squared

b squared = 8 squared

b squared = 8 x 8

b squared = 64 cm squared

b) c squared = a squared + b squared

c squared = 36 + 64

c squared = 100 cm squared

c) square root "c" squared and then square root 100 cm squared

c = 10 cm

## Sunday, February 12, 2012

### Ayra's Pythagorean Post

*The relationship between the*

*lengths of the side of the right triangle. The sum of the areas of the squares attached to the legs of a right triangle equals*

*the area of a square attached to the hypoten*

*use.*

the Pythagorean relationship can be used to show if a triangle is a right triangle.

Left side:

7 squared+6 square= 13 squared

(7x7)+(6x6)=(13x13)

49+36=85

square root of "C" squared= square root of 100cm squared is 10

C=10cmthe sum of the areas of the two smaller squares is 100cm squared.

the triangle is a right triangle.

2. Solve for the missing side length

a squared+b squared= c squared

8 squared+6 squared=11 squared

(8x8)+(6x6)=(11x11)

64+36=121

square root of "C"squared= square root of 121cm squared is 11

C=11cm

the triangle a right triangle.

3. Is this a right triangle? Prove it!!!

a squared + b squared = c squared

8 squared + 6 squared = 11 squared

(8x8) + (6x6) = (11x11)

64 + 36 = 121

It's not a right triangle because it's not equal. The legs aren't equal to the hypotenuse.

### Carlo's Pythagorean Relationship

## Saturday, February 11, 2012

### anton816

B 8 64 6²+8²=10²

C 10 100 36+64=100

## Wednesday, February 8, 2012

### Kate's Pythagoraen Relationship Scribe post

*The relationship between the**lengths of the side of the right triangle. The sum of the areas of the squares attached to the legs of a right triangle equals** the area of a square attached to the hypoten**use.*

the pythagorean relationship can be used to show if a triangle is a right triangle.

Left side:

6 squared+8 square= 10 squared

(6x6)+(8x8)=(10x10)

36+64=100

square root of "C" squared= square root of 100cm squared is 10

C=10cm

the sum of the areas of the two smaller squares is 100cm squared.

the triangle is a right triangle.

"A" squared + "B" squared = "C" squared means

A number times it self so 2 squared means 2x2 and 6 squared is 6x6

8 squared + 6 squared = 11 squared

A squared + B squared = c squared

(8x8) + (6x6) = (11x11)

64 + 36 = 121

the total is 121 cm

12 squared + 5 squared = ???

A squared + b squared = ???

(12x12) + (5x5) = ???

144 + 25 = 169

check mark thing 169 = 13

### natasha's pythagorean relationship

the pythagorean relationship can be used to show if a triangle is a right triangle.

Left side:

6 squared+8 square= 10 squared

(6x6)+(8x8)=(10x10)

36+64=100

square root of "C" squared= square root of 100cm squared is 10

C=10cm

the sum of the areas of the two smaller squares is 100cm squared.

the triangle is a right triangle.

a squared+b squared= c squared

8 squared+6 squared=11 squared

(8x8)+(6x6)=(11x11)

64+36=121

square root of "C"squared= square root of 121cm squared is 11

C=11cm

the triangle a right triangle.

C squared= a squared+b squared

C squared= 12 squared+5 squared

C squared=(12x12)+(5x5)

C squared=144+100

C squared=244 squared

square root of "C" squared= square root of 244 is 15

C square= 15cm