SOLUTION: the hypotenuse of a right triangle is 22.8cm.One leg is double the length of the other leg.what are the lengths of the two legs?

Algebra ->  Trigonometry-basics -> SOLUTION: the hypotenuse of a right triangle is 22.8cm.One leg is double the length of the other leg.what are the lengths of the two legs?      Log On


   

Question 1031105: the hypotenuse of a right triangle is 22.8cm.One leg is double the length of the other leg.what are the lengths of the two legs?
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2%2Bb%5E2=c%5E2
c = 22.8
Let a be the longer leg
a = 2b
substituting we have
%282b%29%5E2%2Bb%5E2=22.8%5E2
4b%5E2%2Bb%5E2=22.8%5E2
5b%5E2=22.8%5E2
divide each side by 5
b%5E2=22.8%5E2%2F5
take the square root of each side
b=sqrt%2822.8%5E2%2F5%29
b = 10.196
a = 2b = 2*10.196 = 20.392