Question

The given diagram can be used to prove the Pythagorean theorem. Which expression represents the total area of the largest square on the diagram?

A) a2 + b2

B) a2 + b2 + c2

C) a2 + 2ab + b2

D) a2 + ab + b2

Answer 1

a2 + b2

area of red square = a2; blue square = b2 -> total area = a2 + b2

Answer 2

C = a² + 2ab + b²

Explanation:

From the diagram above,

Let the dimension of the square be

A (length) = (a + b) and B (breadth) = (a + b).

Area of the square is A*B

A * B = (a + b) * (a + b)

Area = a² + ab + ab + b²

Area = a² + 2ab + b².

Therefore the expression that defines the area of the square is a² + 2ab + b².