math
posted by Elie on .
Make a model of a rectangular prism that is not a cube and has a surface area of 62 cm squared. What are the measurements of this rectangular prism?
I know the formula, is 2ab+2bc+2ac=sa, and I know the answer to this problem... a=5, b=3, and c=2... I did this by trial and error, and I know that there has to be a simpler way. I am trying to teach my 5th grader how to find the solution to this problem, and I don't know how to do it without just doing trial and error. If someone could explain this to me so that I could teach him, I'd really appreciate it. Thanks in advance.

Hmmm. To make things easier, assume you have integer dimensions.
Also, noting that the sum of one of each of the parallel faces is half the area, or 31 in this case.
So, you want three numbers that have factors and add up to 31.
There's still some trial and error, since there are three variables, and only one equation.
You know that at least two of the numbers have to be odd, since you want to end up with three products that add up to 31, and odd number.
So, starting small,
if a=2, then you could have b=3, giving you 2*3 + 2c+3c = 31, or c=5. First Try!
You won't always be so lucky, but by analyzing the information a bit, you can usually cut down on the false starts.