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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 

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