SOLUTION: The hypotenuse equals 23 units, find the size of the other two legs of a right triangle with one leg 3 units more than the other. What is the formula?

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Question 154288: The hypotenuse equals 23 units, find the size of the other two legs of a right triangle with one leg 3 units more than the other. What is the formula?
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the length of the shorter leg, then that of the longer one is x + 3.
Applying the Pythagorean Theorem, we have
x%5E2+%2B+%28x%2B3%29%5E2=23%5E2
Solving for x, we have
x%5E2%2Bx%5E2%2B6x%2B9=529
2x%5E2%2B6x-520=0
x%5E2%2B3x-260=0 (divide both sides by 2)
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ (plug in a=1,b=3,c=-260)
x+=+%28-%283%29+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-260%29+%29%29%2F%282%2A1%29+
x+=+%28-3+%2B-+sqrt%28+9%2B1040+%29%29%2F2+
x+=+%28-3+%2B-+sqrt%28+1049+%29%29%2F2+
So
x+=+%28-3+%2B+sqrt%28+1049+%29%29%2F2+=+14.69
Or
x+=+%28-3+-+sqrt%28+1049+%29%29%2F2=-17.69+ (reject this solution as the length can not be negative)
Thus the length of the shorter leg is 14.69 units, and the length of the longer one is x+3=14.69+3=17.69 units