SOLUTION: The Right Right Triangle What is the largest right triangle with integer length sides (in inches) whose perimeter (measured in inches) has the same numerical value as its area (

Question 1004129: The Right Right Triangle
What is the largest right triangle with integer length sides (in inches) whose perimeter (measured in inches) has the same numerical value as its area (measured in square inches)?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the legs a and b.
The area is
A = (1/2)ab
The perimeter is
P = a + b + sqrt(a^2 + b^2)
so that we need to solve
a + b + sqrt(a^2 + b^2) = (1/2)ab
sqrt(a^2 + b^2) = (1/2)ab - a - b
This might be very tricky to solve...
I tried some values and found 5, 12, and 13 work.

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