Question

The perimeter of a rectangle is 40 inches and each diagonal of the rectangle is 18 inches long. What is the area of this rectangle?

Answer 1

2(x + √(18² - x²)) = 40

x + √(324 - x²) = 20

√(324 - x²) = 20 - x

324 - x² = 400 - 40x + x²

2x² - 40x + 76 = 0

x² - 20x + 38 = 0

x² - 20x + 100 = 62

(x - 10)² = 62

x - 10 = ±√62

x = 10 ± √62

Area = (10 + √62)(10 - √62)

= 100 - 62 = 38