The perimeter and area of the top of the child's desk are 120 inch and 864 inch² respectively.
Explanation
Dimensions of the top of the adult's desk : Length = 54 inches and Width = 36 inches.
As the dimensions of the child's desk are [tex]\frac{2}{3}[/tex] of the dimensions of the adult desk, so....
Length of child's desk [tex]= 54*\frac{2}{3} = 36[/tex] inches and
Width of child's desk [tex]=36*\frac{2}{3}=24[/tex] inches.
So, the perimeter of the top of the child's desk [tex]=2(length+width)= 2(36+24)=120[/tex] inches.
and the area of the top of the child's desk [tex]=length*width=36*24=864[/tex] inch²