Asked by Richard

A child's desk is made so that the dimensions are two-thirds the dimensions of a full-size adult desk.
Suppose the top of the full-size desk measures 54 inches long by 36 inches wide.
What is the perimeter and area of the topof the child's desk?
Answered by Reiny
Areas of similar figures are proportional to the square of the sides

area of larger top = 54x36 = 1944

area of kid's desk/1944 = (2/3)^2 = 4/9
area of kid's desk = (4/9)(1944)
= 864 inches^2

perimeter of big top = 2(54+36) = 180
perimeter of kid's top = (2/3)(180) = 120 inches

or

dimensions of kids top
= (2/3)(54) by (2/3)(36
= 36 by 24

area of little top = 36(24) = 864
perimter of little top = 2(36+24) = 120
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