Problema Solution
rectangle lot whose perimeter is 320 feet is fenced along three sides. An expensive fencing along the lot's length costs $20 per foot. An inexpensive fencing along the two side widths costs only $5 per foot. The total cost of the fencing along the three sides comes to $2140. What are the lots dimensions?
Answer provided by our tutors
let
l = the length of the lot
w = the width of the lot
the perimeter of the rectangle is 320 thus
2(l + w) = 320 divide both sides by 2
l + w = 160
the total cost of the fence along the lots length is: 20*l
the total cost of the two side widths is: 2*w*5 = 10*w
the total cost of the fencing along the three sides comes to $2140
20l + 10w = 2140 divide both sides by 10
2l + w = 214
by solving the system of equations
l + w = 160
2l + w = 214
we find
l = 54 ft
w = 106 ft
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the dimensions of the lot are the length is 54 feet and the width is 106 feet.