SOLUTION: what is the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg

Algebra ->  Triangles -> SOLUTION: what is the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg       Log On


   

Question 946035: what is the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= length of the shortest leg in meters.
Then,
2x%2B6= length of the hypotenuse in meters.
Applying the Pythagorean theorem,
x%5E2%2B24%5E2=%282x%2B6%29%5E2
x%5E2%2B576=4x%5E2%2B24x%2B36
0=4x%5E2-x%5E2%2B24x%2B36-576
0=3x%5E2%2B24x-540
Dividing both sides of the equal sign by 3, we get
0=x%5E2%2B8x-180
Factoring , we get
0=%28x%2B18%29%28x-10%29 ---> system+%7B%7B%28%7Bx=10%2C%22or%22%2Cx=-18%29
Since x , the length of the shortest leg in meters, cannot be a negative number,
the length of the shorter leg is highlight%2810meters%29.