Question

A farmer has 250 ft of fencing and wants to enclose a rectangular area of 3750 ft². What dimensions should she use?

The length of the longer side of the fence is:

The length of the shorter side of the fence is:

Answer 1

Longer 75 , shorter 50

Answer 2

Longer side is 75 feet, shorter side is 50 feet.

Explanation:

Let l be the length of the longer side and w be the length of the shorter side.

2l + 2w = 250, which simplifies to

l + w = 125. Solving for w, we have

w = 125 - l.

lw = l(125-l) = 3750

`{l}^(2) - 125l - 3750 = 0`

`( l - 50)(l - 75) = 0`

l = 75, w = 50