let

l = the original length of the rectangle, l>0

w = the original width of the rectangle, w>0

the length of a rectangle is 2 cm greater than the width:

l = 2 + w

the area of the original rectangle is: A=l*w

l + 4 = the new length (increased by 4 cm)

w + 3 = the new width (increased by 3 cm)

the are of the new rectangle is: A = (l + 4)(w + 3) and it is increased by 88 cm compared the the are of the original rectangle:

(l + 4)(w + 3) = 88 + l*w

plug l = 2 + w into the last equation:

(2 + w + 4)(w + 3) = 88 + (2 + w)*w

by solving we find:

w = 10 cm

click here to see the step by step solution of the equation:

l = 2 + 10

l = 12 cm

he original dimensions of the rectangle are: the length is 12 cm and the width is 10 cm.