(x + y)² and z² + 4(1/2 xy) both represent the area of the outer square and are equal.
Step-by-step explanation:
- Step 1: The below reasons explain why the expression is a true equation.
1. The expression (x + y)² finds the area of the outer square by squaring its side length.
[In the figure, side length of the outer square = x + y and area of a square = (side length)²]
2. The expression z² + 4(1/2 xy) 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 z, the triangles have a base x and height y and area of a triangle = 1/2 base × height]
⇒ So the left hand side and right hand side of the expression is equal.
