Solution Q.18. A sheet of paper is to contain 18 c m 2 of printed matter. The margins at the top and bottom are 2 cm each, and at the sides 1 cm each. Find the dimensions of the sheet which require the least amount of paper. Share with your friends Share 6 Neha Sethi answered this Dear student Le the length of the sheet= x cmBreadth of the sheet= y cmNow, area of sheet=18 cm2⇒xy=18⇒y=18x ...1Now, length of printed portion=x-4 cmBreadth of printed portion=y-2 cmNow area of printed portion=x-4y-2⇒A=xy-2x-4y+8⇒A=18-2x-418x+8⇒A=18-2x-72x+8⇒dAdx=-2+72x2For maxima and minimadAdx=0⇒-2+72x2=0⇒-2x2+72=0⇒x2=36⇒x=6Now,d2Adx2=-144x3d2Adx2x=6=-14463=-23<0So, printed area is maximum at x=6Now, from (1), y=186=3So, length of the sheet=6cmbreadth of the sheet=3cm Regards -18 View Full Answer