Question

Zach is building a new shed shaped like a square prism. He wants the height of the shed to be 2 feet less than the length and width. If he needs the volume to be as close as possible to 3174 ft 3 , what should the length be

Answer 1

`15.394\ \text{feet}`

Explanation:

Let
`x` be the length and width of the base of the prism and,

`y` be the height of the prism.

Now height of the prism is 2 feet less than the length and width.

So
`y=x-2`

Volume of the the square prism is
`3174\ \text{ft}^3`

`x^2y=3174`

Now we graph both the functions.

The point at which they intersect each other is
`(15.394,13.394)`

So, the length of the prism is
`15.394\ \text{feet}`.