SOLUTION: Pythagorean Theorem: side A^2+Side B^2=hypotenuse C^2 (x-2)^2+(x-4)^2=x^2 work: 2x^2-36=x^2 2x^2=x^2+36 x^2=36 Square root both sides x=6 Incorrect though. Not sure

Question 1105103: Pythagorean Theorem:
side A^2+Side B^2=hypotenuse C^2
(x-2)^2+(x-4)^2=x^2
work:
2x^2-36=x^2
2x^2=x^2+36
x^2=36
Square root both sides
x=6
Incorrect though. Not sure what I did wrong.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(x-2)^2 +(x-4)^2 = x^2
:
x^2 -4x +4 +x^2 -8x + 16 = x^2
:
2x^2 -12x +20 = x^2
:
x^2 -12x +20 = 0
:
(x-10) * (x-2) = 0
:
x-10 = 0
x = 10
:
x-2 = 0
x = 2
:
*******************************************************
x = 10 or x = 2, so we have two possible right triangles
8, 6, 10 or 0, -2, 2
we reject the 0, -2, 2 triangle and select 8, 6, 10 triangle
:
check answers by substituting for x in original equation
:
x = 10
(10-2)^2 + (10-4)^2 = 10^2
64 + 36 = 100
100 = 100
:
x = 2
(2-2)^2 + (2-4)^2 = 2^2
4 = 4
:
our answers check
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:
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