The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

Suppose the length is 100x and the width 100y then the new length
=120x and the new width is 120y
The new area =120xX120y=14400xy
Old area = 100xX100y=10000xy
Increase = 4400xy
%increase =(increase/original)X100=(4400xy)/(10000… = 44%

Let:
l = length of original rectangle
w = width of original rectangle
a = area of original rectangle = lw
L = length of enlarged rectangle = 1.2(l)
W = width of enlarged rectangle = 1.2(w)
A = area of enlarged rectangle = LW = 1.2(l) * 1.2(w) = 1.44(lw) = 1.44a

Solution:

................................(A - a)
% increase in area = ----------- * 100
....................................a

................................(1.44a - a)
% increase in area = ----------------- * 100
....................................a


................................0.44a
% increase in area = ---------- * 100
....................................a



% increase in area = 0.44 * 100

% increase in area = 44% <<<<< Answer

44%.