document.write( "Question 924783: if the area of rectangle is 168 centimetres square and its diagonal is 25 centimetre find its length breath and perimeter \n" ); document.write( "
Algebra.Com's Answer #561092 by rothauserc(4718)\"\" \"About 
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let l be the length of rectangle and w be the width, then we have two equations
\n" ); document.write( "l * w = 168
\n" ); document.write( "l^2 + w^2 = 25^2
\n" ); document.write( "solve first equation for l
\n" ); document.write( "l = 168 / w
\n" ); document.write( "substitute for l in second equation
\n" ); document.write( "(168/w)^2 +w^2 = 25^2
\n" ); document.write( "(28224/w^2 +w^2 = 625
\n" ); document.write( "multiply both sides of = by w^2
\n" ); document.write( "28224 +w^4 = 625w^2
\n" ); document.write( "w^4 -625w^2 +28224 = 0
\n" ); document.write( "this equation has the following solution set
\n" ); document.write( "w = (-24, -7, 24, 7)
\n" ); document.write( "we are only interested in positive values of w and in a rectangle l > w
\n" ); document.write( "so we pick w = 7 cm and l is 24 cm
\n" ); document.write( "check answer
\n" ); document.write( "24^2 + 7^2 = 25^2
\n" ); document.write( "576 + 49 = 625
\n" ); document.write( "625 = 625
\n" ); document.write( "answer checks\r
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