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?

169 cm²

Step-by-step 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

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.