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

Answer:

$15.394\ \text{feet}$

Step-by-step 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 $15.394\ \text{feet}$.