Wrong question, Right answer

A bit off topic but I thought this is worth a post.  It's a story of how my room-mate and I solved a problem that was asked wrong.  It all started when my friend, John, asked on skype to help him with a semi-challenging Math problem:

Let Area of a right triangle be 25cm squared. Express the perimeter as a function of the hypotenuse h(p) - John

The actual question is asking to express the hypotenuse as a function of perimeter since his final answer was different than ours. It Steve and I about 2-3 hours to figure out with the first two hours of me on the bed switching Pythagoras and perimeter terms around with no luck. Having nearly given up, I asked John for a hint and he told me to model the problem as such:

First take the hypotenuse and change it such that it has the term - John

Steve and I spent an hour or two and finally believe we figured out. * Note that we had to do it the hard way since the question was asking for the opposite term.

First we start with the Pythagorean theorem:



We know that


We were stuck here for a bit but then I had an eureka! Taking the Perimeter equation



Using the quadratic formula, we come up with the final roots.

John's Answer was the complete other way around requiring only one answer. Our solution to this question may not be the most technical but it was definitely a great feeling of success when we're able to solve the problem the non-intended way.

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