document.write( "Question 988275: I'm in college and I have a question on my math homework and its asking me for the area of a triangle and all the lengths of the sides and its only telling me that the hypotenuse is 3 cm longer than the long side, and the short side is 3 cm shorter than the long side. can you just show me how to set this up? \n" ); document.write( "
Algebra.Com's Answer #608844 by Cromlix(4381)\"\" \"About 
You can put this solution on YOUR website!
Hi there,
\n" ); document.write( "Make the long side = 'x'
\n" ); document.write( "Hypotenuse = x + 3
\n" ); document.write( "Short side = x - 3
\n" ); document.write( "Now by Pythagoras
\n" ); document.write( "(long side)^2 + (short side)^2 = (hypotenuse)^2
\n" ); document.write( "(x)^2 + (x - 3)^2 = (x + 3)^2
\n" ); document.write( "Working out equations;
\n" ); document.write( "x^2 + x^2 - 6x + 9 = x^2 + 6x + 9
\n" ); document.write( "Collect like terms
\n" ); document.write( "x^2 + x^2 - x^2 - 6x - 6x + 9 - 9 = 0
\n" ); document.write( "x^2 - 12x = 0
\n" ); document.write( "x(x - 12) = 0
\n" ); document.write( "x = 12.
\n" ); document.write( "So,
\n" ); document.write( "Hypotenuse = 15cm
\n" ); document.write( "Long side = 12cm
\n" ); document.write( "Short side = 9cm
\n" ); document.write( "Area of triangle = 1/2(base x height)
\n" ); document.write( "Area of triangle = 1/2 (12 x 9)
\n" ); document.write( "Area of triangle = 1/2(108)
\n" ); document.write( "Area of triangle = 54cm^2
\n" ); document.write( "Hope this helps :-) \n" ); document.write( "
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