Question

On moving day, Jorge needs to rent a truck. The length of the cargo space is 12 ft, and the height is 1 ft less than the width. The brochure indicates that the truck can hold 504 ft3. What are the dimensions of the cargo space? Assume that the cargo space is in the shape of a rectangular solid.

Answer 1

12ft
`*`7ft
`*`6ft

Explanation:

Given that truck can hold = 504
`ft^(3)` i.e.

Volume, V = 504
`ft^(3)`

Length of cargo space = 12 ft

Let width of cargo space = w ft

As per question statement:

Let height of cargo space = (w-1) ft

To find: The Dimensions of Cargo Space

Formula for Volume of Cargo Space:

V = Length
`*` Width
`*` Height

Putting the given values and conditions:

504 = 12
`*`
`w * (w-1)`

`\Rightarrow w(w-1) = (504)/(12)\\\Rightarrow w^(2) -w = 42\\\Rightarrow w^(2) -w - 42=0\\\Rightarrow w^(2) -7w +6w -42 =0\\\Rightarrow w(w -7) +6(w -7) =0\\\Rightarrow (w -7)(w+6) = 0\\\Rightarrow w =7, -6`

Dimensions can not be negative, so width, w = 7 ft

Height = (w-1) = 7-1 = 6 ft

So, the dimensions are 12ft
`*`7ft
`*`6ft.