document.write( "Question 924439: In a right triangle, the perimeter is 70, and the sum of the squares of the sides is 1682. Find the lengths of the three sides. Thanks for your help. \n" ); document.write( "
Algebra.Com's Answer #560847 by rothauserc(4718)\"\" \"About 
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There are two solutions to this problem, we are given
\n" ); document.write( "a + b +c = 70 and a^2 +b^2 +c^2 = 1682
\n" ); document.write( "note that a^2 +b^2 = c^2(right triangle), therefore we have
\n" ); document.write( "c^2 +c^2 = 1682
\n" ); document.write( "2c^2 + 1682
\n" ); document.write( "c^2 = 841
\n" ); document.write( "c = 29
\n" ); document.write( "note we are dealing only with positive roots
\n" ); document.write( "now we have
\n" ); document.write( "a +b +29 =70
\n" ); document.write( "a +b = 41
\n" ); document.write( "a^2 +b^2 +841 = 1682
\n" ); document.write( "a^2 +b^2 = 841
\n" ); document.write( "now solve a +b = 70 for b and substitute b in a^2 +b^2 = 841
\n" ); document.write( "a^2 +(41-a)^2 = 841
\n" ); document.write( "a^2 +1681 -82a +a^2 = 841
\n" ); document.write( "2a^2 -82a +840 = 0
\n" ); document.write( "a^2 -41a +420 = 0
\n" ); document.write( "factor this equation
\n" ); document.write( "(a-21)*(a-20) = 0
\n" ); document.write( "a =21 or 20
\n" ); document.write( "our two solutions are
\n" ); document.write( "a=21, b=20, c=29
\n" ); document.write( "a=20, b=21, c=29\r
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