document.write( "Question 118621: A square sheet of Aluminum is placed in the hot sun. It begins to expand very slowly so that its diagonal is increasing at the rate of 1 milimeter per minute. At the moment that the diagonal is 100 milimeters, at what rate is the area increasing? \n" ); document.write( "
Algebra.Com's Answer #86730 by stanbon(75887)\"\" \"About 
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A square sheet of Aluminum is placed in the hot sun. It begins to expand very slowly so that its diagonal is increasing at the rate of 1 milimeter per minute. At the moment that the diagonal is 100 milimeters, at what rate is the area increasing?
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\n" ); document.write( "Let each side of the square sheet be x.
\n" ); document.write( "Let the diagonal be D.
\n" ); document.write( "Then D = (sqrt2)x
\n" ); document.write( "Then dD/dt = (sqrt2)dx/dt
\n" ); document.write( "Since dD/dt = 1ml/min
\n" ); document.write( "So, 1ml/min = (sqrt2)dx/dt
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\n" ); document.write( "Area = x^2
\n" ); document.write( "But x = D/sqrt2
\n" ); document.write( "So, x^2 = D^2/2
\n" ); document.write( "Therefore Area = (1/2)D^2
\n" ); document.write( "--------
\n" ); document.write( "dA/dt = (1/2)(2D)dD/dt
\n" ); document.write( "dA/dt = D(dD/dt)
\n" ); document.write( "dA/dt = 100 ml (sqrt2(ml/min))
\n" ); document.write( "dA/dt = 100sqrt2(ml^2/min)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
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