SOLUTION: The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. The length of the hypotenuse is 6ft more than twice the length of the shorte

Algebra ->  Pythagorean-theorem -> SOLUTION: The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. The length of the hypotenuse is 6ft more than twice the length of the shorte      Log On


   

Question 1088562: The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. The length of the hypotenuse is 6ft
more than twice the length of the shorter leg. Find the side lengths of the triangle.
Find the length of the shorter side
Find the length of the longer side
Find the length of the hypotenuse
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, the length of the shorter leg.

Longer leg, 4%2B2x;
Hypotenuse, 6%2B2x;

x%5E2%2B%282x%2B4%29%5E2=%282x%2B6%29%5E2, use of Pythagorean Theorem (right-triangle)
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x%5E2%2B4x%5E2%2B12x%2B16=4x%5E2%2B24x%2B36
x%5E2%2B12x%2B16=24x%2B36
x%5E2%2B16=12x%2B36
x%5E2-12x-20=0
%28x-2%29%28x-10%29=0
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Either x=2 or x=10


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2, 8, 10
OR
10, 24, 26
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Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The solution by  @josgarithmetic  is  WRONG.  Below find the correct solution. 

x, the length of the shorter leg.


Longer leg, 4%2B2x;
Hypotenuse, 6%2B2x;


x%5E2%2B%282x%2B4%29%5E2 = %282x%2B6%29%5E2, use of Pythagorean Theorem (right-triangle)

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x%5E2%2B4x%5E2%2B16x%2B16 = 4x%5E2%2B24x%2B36

x%5E2%2B16x%2B16 = 24x%2B36

x%5E2-8x-20 = 0

%28x%2B2%29%28x-10%29=0

-

The only positive solution is x=10


Shorter leg = 10 ft.

Longer  leg = 24 ft.

Hypotenuse  = 26 ft.


Check:  10^2 + 24^2 = 676 = 26^2.   Correct.