SOLUTION: How do you figure the length of each side of a right triangle if you have 4x+5, 4x-5 and x

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Question 919894: How do you figure the length of each side of a right triangle if you have 4x+5, 4x-5 and x
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
let sides of a right triangle be a,b, and c where a and b are legs, and c is hypotenuse (longest side)
by Pythagorean theorem: c%5E2=a%5E2%2Bb%5E2
so,if c=4x%2B5, b=4x-5 and a=x, then
%284x%2B5%29%5E2=x%5E2%2B%284x-5%29%5E2
%284x%29%5E2%2B40x%2B25=x%5E2%2B%284x%29%5E2-40x%2B25
cross%28%284x%29%5E2%29%2B40x%2B25=x%5E2%2Bcross%28%284x%29%5E2%29-40x%2B25
40x%2B25=x%5E2-40x%2B25
0=x%5E2-40x-40x%2B25-25
x%5E2-80x=0
x%28x-80%29=0
solutions:
x=0 . ...........we cannot use this solution because a=x
or
%28x-80%29=0 => x=80
then:
highlight%28a=80%29
b=4x-5 => b=4%2A80-5=>b=320-5=>highlight%28b=315%29
c=4x%2B5=>c=4%2A80%2B5=>c=320%2B5=>highlight%28c=325%29
check:
c%5E2=a%5E2%2Bb%5E2
325%5E2=80%5E2%2B315%5E2
105625=6400%2B99225
105625=105625