Butterfly Garden Paths

A large, beautifully-kept rectangular lawn 40 feet by 60 feet is crossed by four straight paths as shown. The paths are all the same width. If the total area of the paths is 736 square feet, how wide is each path?


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So: 2x(60 – 2x) + 2x(40 – 2x) + 4x2 = 736
120x – 4x2 + 80x – 4x2 + 4x2 – 736 = 0
-4x2 + 200x – 736 = 0
x2 – 50x +184 = 0
(x – 4)(x – 46) = 0, so x = 4 feet.


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