Problema Solution
A rancher wants to use 200 feet of fencing to eclose a rectangular area of 1600 square feet. What dimensions should the rectangle have?
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let
l = the length of the rectangle, l>0
w = the width of the rectangle, w>0
P = 200 ft the perimeter of the rectangle is equal to the fencing
A = 1600 ft^2 if the area of the rectangle
since the perimeter P = 2(l + w) we have
2(l + w) = 200 divide both sides by 2
l + w = 100
l = 100 - w
the area of the rectangle is A = l*w that is
l*w = 1600
plug l = 100 - w into the last equations
(100 - w)*w = 1600
by solving we find
w1 = 20 ft
w2 = 80 ft
click here to see the step by step solution of the equation
if the width is 20 ft the length is 100 - 20 = 80 ft.
if the width is 80 ft, for the length we get 100 - 80 = 20 ft, but since the length is bigger or equal to the width the only solutions is:
the length of the rectangle is 80 feet while the width is 20 feet.