document.write( "Question 681763: A right angled triangle has a height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1 centimeters. Find and expression for the base of the triangle. \n" ); document.write( "

Algebra.Com's Answer #422776 by mananth(16946) $\"\"$ $\"About$

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height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1 \r
\n" ); document.write( "\n" ); document.write( "Pythagoras theorem
\n" ); document.write( "hypotenuse^2= base^2+height^2\r
\n" ); document.write( "\n" ); document.write( "base^2= hypotenuse^2-height^2\r
\n" ); document.write( "\n" ); document.write( "=(4x-1)^2-(2x+3)^2\r
\n" ); document.write( "\n" ); document.write( "=16x^2-8x+1-(4x^2+12x+9)\r
\n" ); document.write( "\n" ); document.write( "=16x^2-8x+1-4x^2-12x-9\r
\n" ); document.write( "\n" ); document.write( "=12x^2-20x-8
\n" ); document.write( "=4(3x^2-5x-2)
\n" ); document.write( "=4(3x^2-6x+x-2)
\n" ); document.write( "=4(3x(x-2)+1(x-2))
\n" ); document.write( "=4(3x+1)(x-2)\r
\n" ); document.write( "\n" ); document.write( "base = $\"2sqrt%28%283x%2B1%29%28x-2%29%29\"$ cm\r
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