How would I start a problem like the one below?

A poster is to have an area of 220 $\displaystyle in^2$ with 3 inch margins at the bottom and sides and a 5 inch margin at the top. What dimensions will give the largest printed area? (Give your answers correct to one decimal place.)

Here are my steps so far:

220 = w * h

220 / h = w

A = (w - (3 + 5)) * (h - (3 + 5))

A = (w - 8) * (h - 8)

A = wh - 8h - 8w + 64

A = (220 / h)h - 8h - 8(220 / h) + 64

A = 220 - 8h - 1760 / h + 64

A = 156 - 6h - 1760 / h

A' = -8 - -1*1760 / h^2

A' = -8 + 1760 / h^2

0 = -8 + 1760 / h^2

0 = -8h^2 + 1760

8h^2 = 1760

h^2 = 220

h = 14.8

220 / h = w

220 / 14.8 = 14.8 = w