Problema Solution
A rancher wants to use 200 feet of fencing to enclose a rectangular area of 1600 square feet. What dimensions should the rectangle have.
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let
w = the width of the rectangular area, w>0
l = the length of the rectangular area, l>0
A rancher wants to use 200 feet of fencing means the perimeter of the area is 200 ft:
2(l + w) = 200 divide both sides by 2
l + w = 100
l = 100 - w
the area is 1600 ft^2
l*w = 1600
plug l = 100 - w into l*w = 1600
(100 - w)*w = 1600
by solving we find
w = 20 ft
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l = 100 - 20
l = 80 ft
the width is 20 feet.
the length is 80 feet.