Length of truck is 12 ft and height is 1 ft less than the width. The truck can hold 504 ft^3. What are dimensions of cargo space

Question

**assume that the cargo space is in the shape of a rectangular solid**

a. Write an equation in terms of x that represents the given relationship

b. Solve the equation to find the dimensions of the given shape

Answer 1

The volume of a rectangular solid is

V = l • w • h

Volume equals length times width times height

length = 12

width = x

height = x - 1

volume = 504. Therefore

504 = 12 (x)(x - 1) divide by 12

42 = x(x - 1) or 42 = x^2 - x

x^2 - x - 42 = 0 or (x -7)(x + 6) = 0

x = 7 and/or. X = -6. Negative not posible

x = 7 for width, x - 1 = 6 for the height

and 12 is the length