Pre-calculus math

Question

A crate has the shape of a rectangular prism. The area of the base of the crate is 252 square inches. The length of the crate is 4 inches greater than the width. The height is 2 inches less than the width. What is the volume of the crate in cubic inches?

Answer 1

Since you are given the area of the base=252 can solve for the length and width. let w = width then length is (w+4) so w(w+4)=252 w^2 +4w -252 = 0 now factor and solve

(w+18)(w-14) =0

w=14 discard the solution w=-18 since you can have a negative length

So width = 14

length = w+4 =18

height = w-2 = 12

Volume = l x w x h

Volume = (14)(18)(12)= 3042 sq inches