If two opposite sides of a square are increased by 14 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 72 square meters. find the area of the original square.

Let us call that the original side of the square is called “s”.

So the new dimensions are:

(s – 14) and (s – 7)

The formula for area of rectangle is:

A = l * w

therefore:

72 = (s – 14) * (s – 7)

s^2 – 7s – 14s + 98 = 72

s^2 – 21s = -26

Completing the square:

s^2 – 21s + 110.25 = -26 + 110.25

(s – 10.5)^2 = 84.25

s = 10.5 ± 9.18

s = 1.32, 19.68

s must be bigger than 14, so the correct side of the square is:

s = 19.68 m

So the area of the original square is:

A = s^2 = (19.68 m)^2

A = 387.3 square meters