A rectangular prism has a height of 7.5 cm and a length of 9 cm. If the total surface area is 399 square cm, what is the width of the prism?

Well, the area of the known side is height*length, 7.5*9, and thus 67.5.

Well, since there are two of these sides on a rectangle, we can do 67.5*2 = 135

Now subtract this from the total surface area: 399-135 = 264

 

Now this is where it'll be a little tricky. We know there's four sides left and 264 more surface area left...but not all of these sides are necessarily the same area.

 

If you think about it, one of the sides lengths of two of these squares will have to be 7.5, and one of the side lengths of the other two squares will be 9. Also, the other side legnth for all four of these squares will be the width (or x, because we don't know this yet)

 

So what we can do is set up an equation! Woohoo!

We'll end up with something like

2(7.5*x) + 2(9*x) = 264      (x = width)

2(7.5x)+2(9x)=264

15x+18x=264

33x=264

x = 264/33

x = 8

 

Nice! The width is 8 cm!