SOLUTION: The difference between hypothesis and one side of right angle triangle is 18 cm and third side is

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Question 949210: The difference between hypothesis and one side of right angle triangle is 18 cm and third side is
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
right angle triangle has sides
hypotenuses c
legs a and b
using Pythagorean theorem, we know that:
c%5E2=a%5E2%2Bb%5E2

if the difference between hypotenuses c and one side, let say a, of right angle triangle is 18 cm, then we know that c-a=18=> c=18%2Ba
and third side b is:
%2818%2Ba%29%5E2=a%5E2%2Bb%5E2
18%5E2%2B36a%2Ba%5E2=a%5E2%2Bb%5E2
324%2B36a%2Bcross%28a%5E2%29=cross%28a%5E2%29%2Bb%5E2
324%2B36a=b%5E2
b=sqrt%28324%2B36a%29
b=sqrt%2836%289%2Ba%29%29
b=6sqrt%289%2Ba%29