document.write( "Question 1013551: In right triangle ABC, AC = x, BC = x + 1, and hypotenuse AB = 2x - 1. Find the length of AC only. [only an algebraic solution will be accepted] \n" ); document.write( "
Algebra.Com's Answer #629852 by ankor@dixie-net.com(22740)\"\" \"About 
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In right triangle ABC, AC = x, BC = x + 1, and hypotenuse AB = 2x - 1.
\n" ); document.write( " Find the length of AC only.
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\n" ); document.write( "Using pythag a^2 + b^2 = c^2, where
\n" ); document.write( "a = x, which is AC
\n" ); document.write( "b = (x+1), which is BC
\n" ); document.write( "c = (2x-1), which is the hypotenuse AB
\n" ); document.write( ":
\n" ); document.write( "x^2 + (x+1)^2 = (2x-1)^2
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 + (x^2 + 2x + 1) = 4x^2 - 4x + 1
\n" ); document.write( "combine like terms on the left
\n" ); document.write( "x^2 + x^2 - 4x^2 + 2x + 4x + 1 - 1 = 0
\n" ); document.write( "-2x^2 + 6x = 0
\n" ); document.write( "Factor out -2x
\n" ); document.write( "-2x(x - 3) = 0
\n" ); document.write( "resulting in
\n" ); document.write( "-2x = 0
\n" ); document.write( "and
\n" ); document.write( "x = +3, which is AC
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\n" ); document.write( "See if that works, a=3, b=4, c=5
\n" ); document.write( "3^2 + 4^2 = 5^2
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