Wrong Formulas

Geometry Level 3

While helping my class in math, after drawing two right triangles, I asked the class if anyone knew the area of one of the right triangles on the board.

A bratty kid rose her hand in the air and I called on her. "24." she said. When I asked her how she got her answer, she said, "Easy. I added the three sides together."

I was going to tell her she was wrong when I noticed that it worked for my second triangle too.

The bratty kid had a smug look on her face.

What is the sum of all the lengths of the two right triangles I drew on the board, assuming that one side can be no greater than 20?

Image Credit: Wikimedia ENERGY.GOV

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