SOLUTION: Geometry. The length of one leg of a right triangle is 3in. more than the other. If the length of the hypotenuse is 15 in., what are the lengths of the two legs?

Question 78375: Geometry. The length of one leg of a right triangle is 3in. more than the other. If the length of the hypotenuse is 15 in., what are the lengths of the two legs?
Answer by dolly(163) (Show Source): You can put this solution on YOUR website!
Let the length of 1 leg = x in
So the length of the other leg = (x + 3) in
Then by Pythagorean theorem, the hypotenuse is given by,
x^2 + (x+3)^2 = hyp^2
==> x^2 + (x+3)^2 = 15^2
==> x^2 + x^2 + 6x + 9 = 225 [expanding (x+3)^2 using identity]
==> 2x^2 + 6x + 9 = 225
==> 2x^2 + 6x + 9 - 225 = 0
==> 2x^2 + 6x - 216 = 0
==> x^2 + 3x - 108 = 0 [dividing by 2 throughout]
==> x^2 + 12x - 9x - 108 = 0
==> x(x+ 12) - 9(x+12) = 0
==> (x+12)(x-9) = 0
==> x+12 = 0 or x - 9 = 0
==> x = -12 or x = 9
As length cannot be negative, x = 9
==> one length of the triangle = 9 in
The other leg measures = 9+3
= 12 in

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