document.write( "Question 754382: The larger leg of a right triangle is 3 centimeters longer than its smaller leg. The hypotenuse is 6 centimeters longer than the smaller leg. How many centimeters long is the smaller leg? \n" ); document.write( "
Algebra.Com's Answer #459040 by Cromlix(4381)\"\" \"About 
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Using Pythagoras
\n" ); document.write( " Hypotenuse = (x + 6)
\n" ); document.write( " Longer leg = (x + 3)
\n" ); document.write( " Short leg = x\r
\n" ); document.write( "\n" ); document.write( "Therefore x^2 + (x + 3)^2 = (x + 6)^2
\n" ); document.write( " x^2 + (x^2 + 6x + 9) = (x^2 + 12x + 36)
\n" ); document.write( " 2x^2 + 6x + 9 = x^2 + 12x + 36
\n" ); document.write( " 2x^2 - x^2 + 6x - 12x + 9 - 36 + 0
\n" ); document.write( " x^2 - 6x - 27 = 0
\n" ); document.write( " (x + 3)(x - 9)+ 0
\n" ); document.write( " Therefore x = -3 (No answer)
\n" ); document.write( " x = 9\r
\n" ); document.write( "\n" ); document.write( " Short leg = 9cm\r
\n" ); document.write( "\n" ); document.write( " Hypotenuse^2 = Longer leg^2 + short leg^2
\n" ); document.write( " (9 + 6)^2 = (9 + 3)^2 + 9^2
\n" ); document.write( " 15^2 = 12^2 + 9^2
\n" ); document.write( " 225 = 144 + 81
\n" ); document.write( " 225 = 225 Proved\r
\n" ); document.write( "\n" ); document.write( "Hope this helps
\n" ); document.write( ":-) \n" ); document.write( "
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