document.write( "Question 1200812: the hypotenuse of a right triangle is 3 in. longer than the longer. the shorter leg is 3 in. shorter than the longer leg. find the lengths of the side of the triangle. \n" ); document.write( "
Algebra.Com's Answer #835017 by Theo(13342)\"\" \"About 
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b is the longer leg
\n" ); document.write( "a is the shorter leg
\n" ); document.write( "c is the hypotenuse
\n" ); document.write( "c = b + 3
\n" ); document.write( "a = b - 3
\n" ); document.write( "c^2 = a^2 + b^2 becomes (b+3)^2 = (b-3)^2 + b^2
\n" ); document.write( "subtract (b-3)^2 + b^2 from both sides of the equation to get:
\n" ); document.write( "(b+3)^2 - (b-3)^2 - b^2 = 0
\n" ); document.write( "simplify to get:
\n" ); document.write( "b^2 + 6b + 9 - (b^2 - 6b + 9) - b^2 = 0
\n" ); document.write( "simplify further to get:
\n" ); document.write( "b^2 + 6b + 9 - b^2 + 6b - 9 - b^2 = 0
\n" ); document.write( "combine like terms to gtet:
\n" ); document.write( "-b^2 + 12b = 0
\n" ); document.write( "multiply both sides of this equation by -1 to get:
\n" ); document.write( "b^2 - 12b = 0
\n" ); document.write( "factor out the b to get:
\n" ); document.write( "b * (b-12) = 0
\n" ); document.write( "you get:
\n" ); document.write( "b = 0 or b = 12.
\n" ); document.write( "b can't be equal to 0, so go with b = 12 and see what happens.
\n" ); document.write( "(b+3)^2 - (b-3)^2 - b^2 = 0 becomes:
\n" ); document.write( "(12+3)^2 - (12-3)^2 - 12^2 = 0 which becomes:
\n" ); document.write( "15^2 - 9^2 - 12^2 = 0 which becomes 0 = 0, confirming that b = 12 is good.
\n" ); document.write( "your triangle has a hypotenuse of 15 and a shorter leg of 9 and a longer leg of 12, making it a 9-12-15 triangle, which is similar to a 3-4-5 triangle. \n" ); document.write( "
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