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
