SOLUTION: The hypotense of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the lenghts of the legs of the triangle.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The hypotense of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the lenghts of the legs of the triangle.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 28725: The hypotense of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the lenghts of the legs of the triangle.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
In real right trianlge you would try to find the length by the pythorean theorem.
c%5E2-a%5E2=b%5E2 or c%5E2-b%5E2=a%5E2
Do the smae here. letting a= x+14 and b = x
%2826%29%5E2-%28x%29%5E2=%28x%2B14%29%5E2
676-x%5E2=x%5E2%2B28x%2B196
2x%5E2%2B28x-480
x%5E2%2B14x-240
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=%28-14%2B-sqrt%28%2814%5E2%29-4%2A1%2A-240%29%29%2F%282%2A1%29
Simplfy
you get two solutions.
x=-24 or x=10
10+14=24 (a side)

Hence, the two sides are 10cm and 24 cm.
Paul.