Length: 2w + 59
width: w
diagonal: (2w + 59) + 2 = 2w + 61
Length² + width² = diagonal²
(2w + 59)² + (w)² = (2w + 61)²
(4w² + 118w + 3481) + w² = 4w² + 122w + 3721
5w² + 118w + 3481 = 4w² + 122w + 3721
w² + 118w + 3481 = 122w + 3721
w² - 4w + 3481 = 3721
w² - 4w - 240 = 0
a = 1, b = -4, c = -240
w = [tex][-(b) +/- \sqrt{(b)^{2} - 4(a)(c) }]/2(a)[/tex]
= [tex][-(-4) +/- \sqrt{(-4)^{2} - 4(1)(-240) }]/2(1)[/tex]
= [tex][4 +/- \sqrt{(16 + 960) }]/2[/tex]
= [tex][4 +/- \sqrt{(976) }]/2[/tex]
= [tex][2 +/- 4\sqrt{(61) }]/2[/tex]
= [tex]1 +/- 2\sqrt{(61) }[/tex]
since width cannot be negative, disregard 1 - 2√61
w = 1 + 2√61 ≈ 16.62
Length: 2w + 59 = 2(1 + 2√61) + 59 = 2 + 4√61 + 59 = 61 + 4√61 ≈ 92.24
Answer: width = 16.62 in, length = 92.24 in
