Solve for x given the Surface Area of the right Prism. Round to two decimal spaces. Surface Area =320m^2

Question

Solve for x given the Surface Area of the right Prism. Round to two decimal spaces. Surface Area =320m^2

 

Picture of a Cube shown:

Length (base)= x

Width= 6

Height of cube : 8

 

Answer 1

It isn't actually a "cube" if the dimensions aren't all the same; it's the much snootier "rectangular solid". Every side has a twin directly opposite it, resulting in the following formula:

A_s = 2LW + 2WH + 2LH

In other words, multiply each possible pair of sides then double it. In your case, we plug in everything we know and get:

320 = 2*X*6 + 2*6*8 + 2*X*8

320 = 12X + 96 + 16X

Combine like terms and you get:

320 = 28X + 96                     ...and then isolate by first subtracting:

-96             -96

224 = 28X                               ...then divide by the coefficient.

224 / 28 = 28X / 28

8 = x

Rounding to two decimal places, it's still 8...