SOLUTION: Please show the solution to this triangle problem.Show all calculations. In triangle A,the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer

Algebra ->  Angles -> SOLUTION: Please show the solution to this triangle problem.Show all calculations. In triangle A,the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer      Log On


   

Question 1065267: Please show the solution to this triangle problem.Show all calculations.
In triangle A,the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer leg. Find the length of each side of this right triangle.
Short leg = __________ Long leg = _____________ hypotenuse = _______________

I appreciate all your freely given time and effort. Thank you very much.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the length of shorter side, then
:
longer side length is x + 6 and hypotenuse is x + 12
:
x^2 + (x+6)^2 = (x+12)^2
:
x^2 + x^2+12x+36 = x^2+24x+144
:
x^2 -12x -108 = 0
:
(x + 6) * (x - 18) = 0
:
there are two solutions, x = -6 and x = 18
:
we reject the negative length of x
:
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short leg = 18
:
long leg = 24
:
hypotenuse = 30
:
note that
:
18^2 + 24^2 = 30^2
:
324 + 576 = 900
:
900 = 900
:
our answer checks
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