SOLUTION: A right triangle has a hypoteneuse 11cm long. If the perimeter of the traingle is 25cm, find the lengths of the two other sides.

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Question 350938: A right triangle has a hypoteneuse 11cm long. If the perimeter of the traingle is 25cm, find the lengths of the two other sides.
Answer by dabanfield@earthlink.net(8) (Show Source):
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A right triangle has a hypoteneuse 11cm long. If the perimeter of the traingle is 25cm, find the lengths of the two other sides.
Let a and b be the lengths of the other two sides. By the Pythagorean Theorem we have:
1.) 11^2 = a^2 + b^2
Since the perimeter is 25 we also know a + b + 11 = 25 so:
a = 25 - 11 - b or
a = 14 - b
Substituting 14-b for a in 1.) we have:
121 = (14-b)^2 + b^2
121 = 14^2 - 28*b + b^2 + b^2
121 = 196 - 26*b^2
26*b^2 = 75
b^2 = 75/26
b = sqrt(75/26)
a = 14 - sqrt(75/26)