SOLUTION: the length of a leg of a right triangle is two times the length of the other, and the hypotenuse is 25.What is the length of the longer leg?

Algebra ->  Algebra  -> Pythagorean-theorem -> SOLUTION: the length of a leg of a right triangle is two times the length of the other, and the hypotenuse is 25.What is the length of the longer leg?       Log On

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Question 150635: the length of a leg of a right triangle is two times the length of the other, and the hypotenuse is 25.What is the length of the longer leg?

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length of first leg and y=length of second leg


Since the "length of a leg of a right triangle is two times the length of the other", this means that y=2x. So in this case "y" is the longer leg.


So with the use of Pythagoreans theorem, we get

x%5E2%2By%5E2=25%5E2


x%5E2%2By%5E2=625 Square 25 to get 625


x%5E2%2B%282x%29%5E2=625 Plug in y=2x


x%5E2%2B4x%5E2=625 Square 2x to get 4x%5E2


5x%5E2=625 Add


x%5E2=125 Divide both sides by 5.


x=sqrt%28125%29 Take the square root of both sides. Note: only the positive square root is considered.


x=5%2Asqrt%285%29 Simplify the square root.



So the length of one leg is x=5%2Asqrt%285%29 (which approximates to x=11.18) and the length of the longer leg is y=2%2A5%2Asqrt%285%29=10%2Asqrt%285%29 (which approximates to y=22.36)