Suppose a prism has a length of (x+7), a width of (x), and a height of (x). This prism has the same surface area as an 8-in cube. Find the dimensions of the prism.

Question

anonymous · Answer

We know the surface area of a cube, right? 6x^2, where x is one side's length. In this case, it's 6 * 64 which is 384. Now, the surface area of a (rectangular?) prism is

SA = 2*w*l + 2*w*h + 2*l*h 

where w, l, and h are width, length, and height. Now, you can plug in all of the values for length (x+7), width (x) and height (x) into this formula, and put 384 on the left hand side, because it's the surface area we are given. Now, you can solve for x and get specific values for length, width, and height.