SOLUTION: the hypotenuse of a right triangle is 24 ft long. the length of one leg is 6 feet more than the other. find the length of the legs.

Algebra ->  Pythagorean-theorem -> SOLUTION: the hypotenuse of a right triangle is 24 ft long. the length of one leg is 6 feet more than the other. find the length of the legs.      Log On


   

Question 739103: the hypotenuse of a right triangle is 24 ft long. the length of one leg is 6 feet more than the other. find the length of the legs.
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
c=24
Clearly the side we know the least about is the shortest so...
a=x
the length of one leg is 6 feet more than the other means...
b=x+6
So our equation is:
x%5E2%2B%28x%2B6%29%5E2=24%5E2
so here we go...
x%5E2%2B%28x%5E2%2B12x%2B36%29=576

2x%5E2%2B12x-540=0
divide by 2...
x%5E2%2B6x-270

but this quadratic cannot be factored - so we use the quadratic formula
x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-270%29+%29%29%2F2+


From which the negative solution can be discarded (why?)
therefore...
x=3sqrt%2831%29-3
and so...
{{a=3sqrt(31)-3}}}
{{b=3sqrt(31)+3}}}
c=24