Question

Sam wants to build a fence around her property. The length of

the her fence must be one feet greater than three times its
width and the area of her property is 30 square feet. What is
the maximum width that her fence can be to ensure she
doesn't encroach into her neighbor's property?

Answer 1

3.33ft

Explanation:

Area of the fence = Length * Width

A = LW

Given

Area A = 30ft²

If the length of the her fence must be one feet greater than three times its width, then;

L = 3W + 1

Substotute into the area formula

A = (3W+1)W

30 = 3W²+W

3W²+W - 30 = 0

(3W²+9W)-(10W - 30) =

3W(W+3)-10(W+3) = 0

3W-10 = 0 and W+3 = 0

3W = 10 and W = -3

W = 10/3 and -3

Width cannot be negative

Hence the maximum width that her fence can be to ensure she doesn't encroach into her neighbor's property is 3.33ft