Question

When proving the Pythagorean Theorem, we use the given diagram. The area of the large square is equal to the area all four triangles, plus the area of the inscribed square. Which mathematical sentence demonstrates this? A) a2 + b2 = 1 2 ab + c2 B) a2 + b2 = 4( 1 2 ab) + c2 C) a2 + 2ab + b2 = 1 2 ab + c2 D) a2 + 2ab + b2 = 4( 1 2 ab) + c2

Answer 1

D)

Explanation:

The area of the large square is (a + b)2 or a2 + 2ab + b2. The area of one triangle is

1

2

ab, so the area of all four triangles is 4(

1

2

ab). The area of the inscribed square is c2. The correct answer is a2 + 2ab + b2 = 4(

1

2

ab) + c2.

Answer 2

we know that

[area of one triangle]=a*b/2
[area all four triangles]=4*[a*b/2]------> 4*(1/2)ab

[area of the inscribed square]=c*c-----> c²

[area all four triangles +area of the inscribed square]=4*(1/2)ab+c²----> equation 1

[area of the larger square]=(a+b)*(a+b)-----> a²+2ab+b²-----> equation 2

equals 1 and 2

4*(1/2)ab+c²= a²+2ab+b²

therefore

the answer is the option
D) a2 + 2ab + b2 = 4( 1/2 ab) + c2