SOLUTION: In a right triangle the two legs are each 5 less than the hypotenuse. What is the hypotenuse?

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Question 453406: In a right triangle the two legs are each 5 less than the hypotenuse. What is the hypotenuse?
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
let hypotenuse be x
the legs are (x-5)
By pythagoras theorem
(x-5)^2+(x-5)^2=x^2
x^2-10x+25+x^2-10x+25=x^2
x^2-20x+50=0
Find the roots of the equation by quadratic formula

a= 1 ,b= -20 ,c= 50

b^2-4ac=400-200
b^2-4ac=200
sqrt%28200%29=14.14
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=(20+14.14)/2
x1= 17.07
x2=(20-14.14)/2
x2= 2.93
x2 is not possible
hyptenuse = 17.07