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?

notsmart2.0 Feb 14, 2020

#1**+4 **

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?

Area of the largest square is A = 338 cm²/ 2 = 169 cm²

Dragan Feb 14, 2020

#2**+1 **

Let PR = z

Let PQ = y

Let QR = x

We know from the Pytagorean Theorem that QR^2 + PQ^2 = PR^2 → (x^2 + y^2) = z^2 (1)

But we also know that

(x^2 + y^2) + z^2 = 338 (2) sub (1) into (2) and we have that

z^2 + z^2 = 338

2z^2 = 338 divide both sides by 2

z^2 = 169 = area of largest square

CPhill Feb 14, 2020