Question

A rancher wants to fence in an area of 1,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. Find a function that models the amount of fencing in terms of the width of the field, w, where w is the measurement of the fence down the middle of the field.

Answer 1

f(w) = 3w + 2,000,000/w

Explanation:

We know that the area of a rectangle is the product of its length and width:

A = LW

Filling in the given values lets us write an expression for the length of the field.

1,000,000 = Lw

L = 1,000,000/w

Since there are 3 fences of length w and two of length L, the total perimeter fence length is the sum ...

f(w) = 3w + 2(1,000,000)/w

Combining the constants, we have a function for the perimeter fence length in terms of the width of the field:

f(w) = 3w +2,000,000/w