DAT question of the day help

[mis_gnomer]

I was looking at datquestionoftheday.com in the math section and I couldn't figure out how to set up the problem. The site gives the answer and the brief explanation but I'm still confused as to how you set it up. Can any of my mathematically gifted pre-dents help me out? Thanks, guys.
Here's a link to the question, I'm looking at the one from August 3rd:
http://datquestionoftheday.com/category/math/

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[Carbohydrates]

Call the right triangle with 3 side a,b,c and c is the hypotenus.
Area = 1/2 ab = 30
=> ab = 60
Perimeter = a+b+c=30
Also pythagorean theory :
a^2 + b^2 = c^2

Then you can solve for c by sustituting back and forth between 3 equations.

Or you can backsolve by pick the number in the answer and see which one give the correct number and fit with all the equations above.