SOLUTION: The hypotenuse of the right triangle is 26. One leg is 4 more than twice the other leg. Determine the length of the longer leg.

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Question 888505: The hypotenuse of the right triangle is 26. One leg is 4 more than twice the other leg. Determine the length of the longer leg.
Found 2 solutions by Theo, harpazo:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x = one of the legs.
let y = the other leg.
pythagorus says:
x^2 + y^2 = 26^2
y = 2x + 4
x^2 + y^2 = 26^2 becomes:
x^2 + (2x+4)^2 = 26^2
simplify to get:
x^2 + 4x^2 + 16x + 16 = 676
combine like terms to get:
5x^2 + 16x + 16 = 676
subtract 676 from both sides to get:
5x^2 + 16x - 660 = 0
factor to get:
(x-10)(5x+66) = 0
solve for x to get:
x = 10 or x = -66/5
x can't be negative, so x = 10
if x = 10, then 2x+4 = 24
x = 10
y = 24
10^2 + 24^2 = 100 + 576 = 676 = 26^2
all is good.
one leg is 10.
the other leg is 24.
the leg of 24 is 4 more than twice the leg of 10.

Answer by harpazo(655) (Show Source):
You can put this solution on YOUR website!
Leg 1 = x
Leg 2 = 2x + 4
Hypotenuse = 26
Here is the set up equation:
x^2 + (2x + 4)^2 = (26)^2
Take it from here to solve for x.