document.write( "Question 252661: FIND THE DIMENSIONS OF A RECTANGLE WHOSE PERIMETER IS 76CM THAT WILL GIVE THE MAXIMUM AREA. \n" ); document.write( "
Algebra.Com's Answer #184687 by palanisamy(496)\"\" \"About 
You can put this solution on YOUR website!
Let x and y be the sides of the rectangle.
\n" ); document.write( "Then, its perimeter 2x+2y = 76
\n" ); document.write( " 2y = 76-2x
\n" ); document.write( " y = (76-2x)/2
\n" ); document.write( " y = 38-x ...(1)
\n" ); document.write( "The area of the rectangle is
\n" ); document.write( " A = xy
\n" ); document.write( " A = x(38-x)
\n" ); document.write( " A = 38x-x^2
\n" ); document.write( "Differentiating with respect to x,
\n" ); document.write( " dA/dx = 38-2x
\n" ); document.write( "For maximum or minimum value of A,
\n" ); document.write( " dA/dx = 0
\n" ); document.write( " 38-2x = 0
\n" ); document.write( " 2x = 38
\n" ); document.write( " x = 38/2
\n" ); document.write( " x = 19
\n" ); document.write( "Sustituting in (1), we get
\n" ); document.write( " y = 38-19 = 19
\n" ); document.write( "Therefore the dimensions are 19,19 \n" ); document.write( "
\n" );