Question

~A certain rectangular prism has a height of h inches, a width that is 3 inches less than its height, and a length that is 4 inches more than its height. Ifthe area ofthe base of the prism is 60 square inches, what is the volume of the prism, in cubic inches?

Answer 1

Answer:

Volume = 480 cubic inches

Explanation:

We have the following relationships to work with

width w = h -3

length l = h + 4

area of base of prism a = l x w = 60  (1)

area of base in terms of h = (h-3)(h+4) =h² -3h + 4h -12 (2)

Setting (1) = (2) gives

h² + h -12 =60

h² + h -72 = 0

Factoring the LHS we get

(h+9)(h-8) = 0

The solutions for h are

h + 9 = 0 ==> h = -9

h - 8 = 0 ==> h = 8

Since h cannot be negative, h = 8 inches

Volume = base area x h = 60 x 8 = 480 cubic inches

Note

We do not have to calculate length and width separately, but if so,

w = 8 -3 = 5

l = 8 + 4 = 12