SOLUTION: The hypotenuse of a right triangle is 13 units. If the length of one leg is 2 more than twice the other, then what are their lengths?

Click here to see ALL problems on Triangles

Question 527470: The hypotenuse of a right triangle is 13 units. If the length of one leg is 2 more than twice the other, then what are their lengths?
Found 3 solutions by Alan3354, nerdybill, stanbon:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
5 & 12

Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is 13 units. If the length of one leg is 2 more than twice the other, then what are their lengths?
Let x = one leg
then
2x+2 = other leg
.
applying Pythagorean theorem:
x^2 + (2x+2)^2 = 13^2
x^2 + (2x+2)(2x+2) = 169
x^2 + 4x^2+8x+4 = 169
5x^2+8x+4 = 169
5x^2-25x+33x-165 = 0
(5x^2-25x)+(33x-165) = 0
5x(x-5)+33(x-5) = 0
(x-5)(5x+33) = 0
x = {-33/5, 5}
Throw out negative solution (extraneous) leaving:
x = 5 units (one leg)
.
other leg:
2x+2 = 2(5)+2 = 10+2 = 12 units

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is 13 units. If the length of one leg is 2 more than twice the other, then what are their lengths?
-------
leg 1: x
leg 2: 2x+2
------------------
Equation:
x^2 + (2x+2)^2 = 13^2
x^2 + 4x^2 + 8x + 4 = 169
5x^2 + 8x - 165 = 0
---
Use the quadratic formula to solve:
x = 5
----
leg 1: x = 5
leg 2: 2x+2 = 12
===================
Cheers,
Stan H.