document.write( "Question 17860: A right triangle has side lengths that are consecutive even integers. Use the pythagorean theorem to find the lengths of those sides. Please help! \n" ); document.write( "
Algebra.Com's Answer #8628 by whisper(27)\"\" \"About 
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Let's start by representing the three sides of the triangle:
\n" ); document.write( "x
\n" ); document.write( "x+1
\n" ); document.write( "x+2
\n" ); document.write( "Now let's look at the Pythagorean Theorem:
\n" ); document.write( "a^2+b^2=c^2 where a,b are sides of a right triangle and c is the hypoteneuse.
\n" ); document.write( "Now we set up the equation:
\n" ); document.write( "x^2+(x+1)^2=(x+2)^2
\n" ); document.write( "x^2+x^2+2x+1=x^2+4x+4
\n" ); document.write( "2x^2+2x+1=x^2+4x+4
\n" ); document.write( "Now let's get everything on one side of the equation:
\n" ); document.write( "2x^2-x^2+2x-4x+1-4=x^2-x^2+4x-4x+4-4
\n" ); document.write( "x^2-2x-3=0
\n" ); document.write( "Factor:
\n" ); document.write( "(x-3)(x+1)=0
\n" ); document.write( "x-3=0 or x+1=0
\n" ); document.write( "x=3 lr x = -2
\n" ); document.write( "x cannot be negative therefore x =3
\n" ); document.write( "If x=3 then
\n" ); document.write( "x+1=4
\n" ); document.write( "x+2=5
\n" ); document.write( "and you have a 3,4,5 triangle.
\n" ); document.write( "please don't hesitate to ask if you have further questions! \n" ); document.write( "
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