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Let c = the hypotenuse and a and b the other two legs.
From the problem description, you can write:
Rewrite these in terms of a and b to get:
Now you can use the Pythagorean theorem to find c, the hypotenuse:
Substitute the two equations above for a and b:
from both sides.
Solve this quadratic by factoring:
, so then...
Discard the first solution
as c must be greater than 8 or else you have one leg of the triangle equal to zero!
So, the hypotenuse is 20 and the other two legs are a=12 and b = 16.
Substitute c = 20, a = 12, and b = 16.