If the perimeter of a rectangular flag is 34 in. And the diagonal is 13 in., then what are the length and width?

Perimeter (P) = 2L + 2w

34 = 2L + 2w

17 = L + w

17 - L = w

L² + w² = d²

L² + (17 - L) ² = 13²

L² + 289 - 34L + L² = 169

2L² - 34L + 120 = 0

L² - 17L + 60 = 0

(L - 5) (L - 12) = 0

L - 5 = 0 L - 12 = 0

L = 5 L = 12

17 - L = w ⇒ 17 - 5 = 12 or 17 - 12 = 5

Answer: width = 5 in, length = 12 in