Question

The figures below show two different ways of arranging four identical triangles of grey poster board on top of a white square. The square has sides equal to x + y, while the hypotenuse of each triangle is represented by the variable c.
Hazel wrote the following statements to prove that c2 = x2 + y2.
1. Area of the four grey triangles inside figure A = 4(1/2xy)=2xy
2. Area of the white square inside figure A = c2
3. Area of figure A = c2 + 2xy
4. Area of the four grey triangles inside figure B = 4xy
5. Area of the two white squares inside figure B = x2+ y2
6. Area of figure B = x2+ y2 +

Answer 1

7. Area of figure A = area of Figure B, hence c2 + 2xy = x2+ y2 + 4xy
8. Therefore, c2 = x2+ y2
Which is the first incorrect statement in Hazel’s proof?

Answer 2

A.) Statement 6
B.) Statement 7
C.) Statement 4
D.) Statement 5

Answer 3

@zepp

Answer 4

that c2 = x2 + y2.

Is that \(\large c^2=x^2+y^2\)?

Answer 5

yes

Answer 6

That looks like he wants to prove the pythagorean's theorem :)

Answer 7

what does that mean?

Answer 8

6. Area of figure B = x2+ y2 +

What's after the plus sign? D:

Answer 9

4xy

Answer 10

Okay, found the mistake :D

Let's analyse every step :)

Answer 11

1. Area of the four grey triangles inside figure A = 4(1/2xy)=2xy

Does that one sound right to you?

Answer 12

yes?

Answer 13

Alright, second one?

2. Area of the white square inside figure A = c2

Answer 14

yes

Answer 15

Now 3. Area of figure A = c2 + 2xy

Answer 16

yes

Answer 17

Okay, now, don't looks at Hazel's statements, I want you to solve figure B by yourself, can you find the area of the grey section and the white section?

Answer 18

how do i find it?

Answer 19

How do you find the area of a rectangle?