Mathematical Studies

A right triangle has three sides known to be
(x-5)
(2x+1)
and 2x.

By use of the pythagorean theorem show how the sides of the triangle can yield the equation: x^2-14x+24=0

this is my work below:
(x-5)^2+(2x+1)^2=2x^2
which expanded is:
(x^2-10x+25)+(4x^2+4x+1)=2x^2

i don't understand how that would give you x^2-14x+24=0.

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asked by Andre
  1. They do not say which is the hypotenuse. We need to figure that out.
    x-5 must be the smallest, all it a
    2x is next biggest, call it b
    2x+1 is biggest, the hypotenuse, call it c
    a^2 = (x-5)^2 = x^2 -10x+25 check
    b^2 = 4 x^2 check
    so
    a^2 + b^2 = 5 x^2 -10x+25
    NOW
    c^2 = 4x^2 +4 x +1 check with you
    and we know a^2+ b^2 = c^2
    so
    5 x^2 - 10 x + 25
    = 4 x^2 + 4x + 1
    so
    x^2 -14 x +24 = 0 Yeah !!

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    posted by Damon
  2. thank you!

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    posted by Andre

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