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?

Click here to see ALL problems on Triangles

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