document.write( "Question 678160: If the perimeter of a right angle triangle equals 30cm, and its area is 30cm squared.
\n" ); document.write( "Find the length of the sides. \n" ); document.write( "
Algebra.Com's Answer #421207 by sachi(548)\"\" \"About 
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let AB & AC are two legs of the triangle angle A=90 deg & BC is hypotenuse
\n" ); document.write( "so AB^2+AC^2=BC^2...........1
\n" ); document.write( "the perimeter of a right angle triangle equals 30 cm
\n" ); document.write( "so AB+BC+CA=30..............2
\n" ); document.write( "its area is 30cm squared.
\n" ); document.write( "so 1/2*AB*AC=30
\n" ); document.write( "or AB*AC=60................3
\n" ); document.write( "from 2
\n" ); document.write( "AB+AC=30-BC
\n" ); document.write( "squaring both sides
\n" ); document.write( "AB^2+AC^2+2AB*AC=900+BC^2-2*30*BC
\n" ); document.write( "substituting the values from 1&3
\n" ); document.write( "BC^2+2*60=900+BC^2-60BC
\n" ); document.write( "or 60BC=900-120=780
\n" ); document.write( "or BC=13 ans
\n" ); document.write( "now above eqns 1&2modified to
\n" ); document.write( "AB^2+AC^2=13^2=169..........4
\n" ); document.write( "now (AB-AC)^2=AB^2+AC^2-2AB*AC=169-2*60=49
\n" ); document.write( "or AB-AC=+/-7......5
\n" ); document.write( "from eqn 2
\n" ); document.write( "AB+13+AC=30
\n" ); document.write( "or AB+AC=30-13=17.....6
\n" ); document.write( "adding eqns 5&6
\n" ); document.write( "2AB=24 or 10
\n" ); document.write( "so AB= 12 or 5 ans
\n" ); document.write( "putting these values in eqn 6
\n" ); document.write( "AC=5 or 12 ans
\n" ); document.write( "so AB=12 BC-13 & AC=5 one set solns
\n" ); document.write( "& AB=5 BC-13 & AC=12 the other set solns
\n" ); document.write( "sorry for the mistake in earlier soln
\n" ); document.write( "thnx\r
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