Question

Angle PQR is a right angle. The three quadrilaterals shown are squares. The sum of the areas of the three squares is 338 square centimeters. What is the number of square centimeters in the area of the largest square?

Answer 1

169 cm²

Explanation:

Recall that the area of the largest square is |PR|²

Also recall from Pythagoras Theorem that:

|PQ|² +|QR|² =|PR|² ---->1

Also we have that the sum of the areas of the three squares is 338 square centimeters.

This implies that:

|PQ|² +|QR|² +|PR|²=338---->2

Put equation (1) into (2)

|PR|²+|PR|²=338

Simplify to get:

2|PR|²=338

Divide both sides by 2 to get:

|PR|²=338

|PR|²=169