SOLUTION: The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle

Algebra ->  Pythagorean-theorem -> SOLUTION: The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle      Log On


   

Question 853239: The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle
Answer by hovuquocan1997(83) About Me  (Show Source):
You can put this solution on YOUR website!
Let the long leg of this right triangle be "x"
Then you will have the short leg is "x-5" and the hypotenuse is "x+5"
Use Pythagorean Theorem, you will have:
%28x-5%29%5E2+%2B+x%5E2+=+%28x%2B5%29%5E2
x%5E2+-10x+%2B+25+%2B+x%5E2+=+x%5E2+%2B+10x+%2B+25
2x%5E2+-+10x+%2B+25+=+x%5E2+%2B+10x+%2B+25
x%5E2+-+20x+=+0
x%28x-20%29+=+0
x = 0 or x = 20
But since a side of a triangle can't be 0, x=20
So you have the long leg of the triangle is 20
The short leg will be 20-5 = 15
The hypotenuse will be 20+5 = 25
TA-DAH
:D