document.write( "Question 204200: The area of a rectangle is 6, and its diagonal is sqrt{37}. Find its dimensions and perimeter \n" ); document.write( "
Algebra.Com's Answer #154171 by nerdybill(7384)\"\" \"About 
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The area of a rectangle is 6, and its diagonal is sqrt{37}. Find its dimensions and perimeter
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\n" ); document.write( "Let x = width
\n" ); document.write( "and y = length
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\n" ); document.write( "From Pythagorean theorem
\n" ); document.write( "x^2 + y^2 = 37 (equation 1)
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\n" ); document.write( "From the area:
\n" ); document.write( "xy = 6 (equation 2)
\n" ); document.write( "Solve equation 2 for y:
\n" ); document.write( "y = 6/x
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\n" ); document.write( "Substitute aboe into equation 1 and solve for x:
\n" ); document.write( "x^2 + y^2 = 37
\n" ); document.write( "x^2 + (6/x)^2 = 37
\n" ); document.write( "x^2 + (36/x^2) = 37
\n" ); document.write( "x^4 + 36 = 37x^2
\n" ); document.write( "x^4 - 37x^2 + 36 = 0
\n" ); document.write( "(x^2-36)(x^2-1) = 0
\n" ); document.write( "x = {1, 6}
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\n" ); document.write( "Therefore, dimensions are
\n" ); document.write( "1 feet by 6 feet
\n" ); document.write( "Perimeter:
\n" ); document.write( "2(6+1) = 14 feet
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