document.write( "Question 844101: The longest side of a right triangle is 3 less than 4 times the shortest side. The third side measures 24 inches. Find the length of the shortest side. \n" ); document.write( "
Algebra.Com's Answer #508561 by lwsshak3(11628)\"\" \"About 
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The longest side of a right triangle is 3 less than 4 times the shortest side. The third side measures 24 inches. Find the length of the shortest side.
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\n" ); document.write( "let x= shortest side
\n" ); document.write( "4x-3= longest side=hypotenuse
\n" ); document.write( "by the pythagorean theorem
\n" ); document.write( "x^2+24^=(4x-3)^2
\n" ); document.write( "x^2+576=16x^2-24x+9
\n" ); document.write( "15x^2-24x-567=0
\n" ); document.write( "solve for x by quadratic formula:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "a=15, b=-24, c=567
\n" ); document.write( "ans:
\n" ); document.write( "x=-27/5 (reject)
\n" ); document.write( "or
\n" ); document.write( "x=7
\n" ); document.write( "length of the shortest side=7
\n" ); document.write( "check:
\n" ); document.write( "x^2+24^2=49+576=625 (sum of sides squared)
\n" ); document.write( "(4x-3)^2=25^2=625 (hypotenuse squared)\r
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