(a + b)² and c² + 4(1/2 ab) both represent the area of the outer square and are equal.
Explanation:
- Step 1: The below reasons explain why the expression is a true equation.
1. The left hand side expression (a + b)² finds the area of the outer square by squaring its side length.
[In the figure, side length of the outer square = a + b and area of a square = (side length)²]
2. The right hand side expression c² + 4(1/2 ab) finds the area of the outer square by adding the area of the inner square and the four triangles.
[In the figure the length of the inner square is c, the triangles have a base a and height b and area of a triangle = 1/2 base × height]
So the left hand side and right hand side of the expression is equal.