SOLUTION: The hypotenuse of a right triangle is 3cm longer than twice the length of the shorter leg. The longer leg measures 12 cm. Find the lengths of the shorter leg and the hypotenuse.

Click here to see ALL problems on Triangles

Question 491996: The hypotenuse of a right triangle is 3cm longer than twice the length of the shorter leg. The longer leg measures 12 cm. Find the lengths of the shorter leg and the hypotenuse.
I've tried setting up an equation for this problem but it's not working.
The equation I've tried is
But it's still not working.
Can you please help me with this problem with an explanation please.
Thank You So Much!
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is 3cm longer than twice the length of the shorter leg. The longer leg measures 12 cm. Find the lengths of the shorter leg and the hypotenuse.
.
Let x = length of shorter leg
then
2x+3 = hypotenuse
12 = longer leg
.
Applying Pythagorean theorem:
x^2 + 12^2 = (2x+3)^2
x^2 + 144 = (2x+3)(2x+3)
x^2 + 144 = 4x^2+12x+9
144 = 3x^2+12x+9
0 = 3x^2+12x-135
0 = x^2+4x-45
0 = (x+9)(x-5)
x = {-9, 5}
we can throw out the -9 solution leaving:
x = 5 cm (short leg)
.
hypotenuse:
2x+3 = 2(5)+3 = 10+3 = 13 cm