SOLUTION: In a right angle triangle, hypotenuse is 4cm more than the smallest side and 2cm less than the third side.Find its perimeter

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Question 940066: In a right angle triangle, hypotenuse is 4cm more than the smallest side and 2cm less than the third side.Find its perimeter
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
From Pythagorean theorem,
H%5E2=%28H-2%29%5E2%2B%28H-4%29%5E2
H%5E2=H%5E2-4H%2B4%2BH%5E2-8H%2B16
H%5E2=2H%5E2-12H%2B24
H%5E2-12H%2B20=0
%28H-2%29%28H-10%29=0
Two solutions:
H-2=0
H=2
However subtracting 2 and 4 from this value would lead to zero length and negative length sides.
H-10=0
H=10
So then,
P=H%2BH-2%2BH-4
P=3H-6
P=3%2810%29-6
P=30-6
P=24cm