Question

The surface area of the rectangular prism below is 286in2. Find the height.

Answer 1

Answer: $7in$

Step-by-step explanation:

$Formula: A=2(wl+hl+hw)$

Solve for h;

Let's begin by dividing by 2.

$\frac{A}{2}=wl+hl+hw$

Subtract wl because it's the only term that doesn't have h.

$\frac{A}{2}-wl=hl+hw$

Plug your values into the formula.

$\frac{286in^2}{2}-(5in)(9in) =h(9in)+h(5in)\\143in^2-45in^2=9inh+5inh\\98in^2=14inh$

Divide by 14 to isolate h.

$\frac{98in^2}{14in}=h$

$7in=h$