we will assume that the garden is rectangular and that the tool shed is taking one of the lengths of the garden

let

w = the width of the garden, w>0

l = the length of the garden, l>0

you have 180 yards of fencing to use on three sides of a garden:

l + 2w = 180

l = 180 - 2w

a. What is the maximum area that you can fence?

the area A = width*length that is

A = w*l

plug l = 180 - 2w into the last euqation:

A = w(180 - 2w)

A = -2w^2 + 180w

We need to find the maximum of the parabolic function A(w) = -2w^2 + 180w

A max = c - (b^2/4a), where a = -2, b = 180, c = 0

A max = 0 - 180^2/(4*(-2))

A max = 4,050 yd^2 is the maximum area you can fence

b. What are the dimensions of the garden?

w = - b/2a

w = - 180/(2*(-2))

w = 45 yd

l = 180 - 2*45

l = 90 yd

the dimensions of the garden are 45 yd and 90 yd.