Question

what's the thickness of a rectangle prism with a height of 12 inches, a width of 8 inches and surface area 992 square inches?

Answer 1

Thickness of rectangle prism is 20 inches.

Explanation:

Given:

Surface area of rectangular prism, A = 992 sq inches.

Height, h = 12 inches

Width, w = 8 inches

To find:

Thickness / length of prism,
`l` = ?

Solution:

First of all, let us learn the formula for surface area of a rectangular prism.

Formula for surface area of a prism is given as:

`A=2(wl+hl+hw)`

As there are 6 faces, each face is a rectangle and area of all the faces is considered in the formula. It is just like a cuboid like structure.

Putting all the given values in the formula to find the value of
`l`:

`992=2(8l+12l+8 * 12)\\\Rightarrow 496 = 20l + 96\\\Rightarrow 20 l =496-96\\\Rightarrow 20 l =400\\\Rightarrow l = (400)/(20)\\\Rightarrow l = 20\ inches`

So, the answer is Thickness of rectangle prism is 20 inches.