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The width of a rectangle is 6 kilometers less than twice its length If its area is 140 square kilometers find the dimensions of the rectangle?
The width (w) = 2 x the length (l) - 6 : w = 2l - 6
But the area (w x l) = 140, substituting for w gives
(2l - 6) x l = 140 : 2l² - 6l - 140 = 0
Solving for the roots of a quadratic equation gives :
l = 6 ± √(6² + 1120) ÷ 4 = (6 ± 34) ÷ 4
Only the positive root applies so :
l = (6 + 34)÷ 4 = 10 and by substitution w = (2 x 10) - 6 = 14
The dimensions are width 14 km : length 10 km.
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