document.write( "Question 275310: The legs of a right triangle are represented by x and x+2, and the hypotenuse is 10. Find the area of the triangle. \n" ); document.write( "
Algebra.Com's Answer #200818 by dabanfield(803)\"\" \"About 
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The legs of a right triangle are represented by x and x+2, and the hypotenuse is 10. Find the area of the triangle.\r
\n" ); document.write( "\n" ); document.write( "By the Pythagorean Theorem we have:\r
\n" ); document.write( "\n" ); document.write( "x^2 + (x+2)^2 = 10^2
\n" ); document.write( "x^2 + x^2 + 4x + 4 = 100
\n" ); document.write( "2x^2 + 4x + 4 = 100
\n" ); document.write( "x^2 + 2x + 2 = 50
\n" ); document.write( "x^2 + 2x - 48 = 0
\n" ); document.write( "(x+8)*(x-6) = 0\r
\n" ); document.write( "\n" ); document.write( "x+8 = 0 or x-6 = 0 so x = -8 or x = 6. We need x to be positive so x=6.\r
\n" ); document.write( "\n" ); document.write( "The two legs of the triangle then are 6 and 6+2 = 8. Since it's a right triangle the legs are the base and the height so the area equals 1/2*(base*height) or 1/2*6*8 = 24. \r
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