Greta wants to build a rectangular garden. she plans to use a side of a ride for one side of the garden, so she will not place fencing along this side of the garden. she has 92 yards of fencing material.
what is the maximum area in square yards that will be enclosed?

1058 yd²

Step-by-step explanation:

Let the length be l while width be w

We fence two parts of width but only one side for length since fencing is done only on three parts

Perimeter will then be w+w+l=2w+l=92 yards

Area is l*w

From perimeter

2w+l=92

Making l the subject of the formula then

l=92-2w

Then since area is lw, substituting l with 92-2w we obtain

A=(92-2w)w=92w-2w²

A=92w-2w²

The first derivative with respect to w will be

92-4w=0

4w=92

w=92÷4=23

Since l=92-2w then l=92-2(23)=46

Area then is 23*46=1058 yd²