Question

What is the length of$\overline{XY}$ . (Figure is not drawn to scale.)

Answer 1

Given that XABC is a square of side 36 & EDYB is a square if side 12. So CB^bar = XA^bar = 36, BY^bar = ED^bar = 12, XC^bar = XA^bar = 36 therefore CY^bar = CB^bar + BY^bar = 36 + 12 = 48 Now apply theorem on right angle delta XCY, we get XC^bar + CY^bar^2 = XY^bar^2 or, XY^bar^2 = 36^2 + 48^2 = 36 times 36 + 48 times 48 = 12 times 12 (3 times 3 + 4 times 4) = 12^2 times 5^2 or, XY^bar = 12 times 5 = 60