SOLUTION: Right triangle with the longer leg 6 cm more than the shorter leg and the hypotenuse 12 cm more than the shorter leg. How long are the sides of the triangle?

Algebra ->  Pythagorean-theorem -> SOLUTION: Right triangle with the longer leg 6 cm more than the shorter leg and the hypotenuse 12 cm more than the shorter leg. How long are the sides of the triangle?      Log On


   

Question 1048019: Right triangle with the longer leg 6 cm more than the shorter leg and the hypotenuse 12 cm more than the shorter leg. How long are the sides of the triangle?
Answer by mathslover(157) About Me  (Show Source):
You can put this solution on YOUR website!
Let the shorter leg be x
Longer leg = x+6
Hypotenuse=x+12
Using the Pythogras theorem on right triangles
Sum of squares of the sides = square of the hypotenuse
x%5E2+%2B+%28x%2B6%29%5E2+=+%28x%2B12%29%5E2
=> x%5E2+%2B+x%5E2+%2B12x%2B+36+=+x%5E2+%2B24x+%2B144
=>x%5E2+%2B+x%5E2+-x%5E2+%2B+12x+-24x+%2B36-144+=0 Grouping the like terms on one side
=>x%5E2+-12x+-108+=0
=>+x%5E2+-18x+%2B+6x+-108+=0
=>%28x-18%29%28x%2B6%29=0
This gives us x=18 and x=-6
Ignoring -6 as length cannot be negative
SIdes are 18, 24 and 30 ( x, x+6 and x+12)