The equations of two sides of a square are 7x + 24y – 72 = 0 and 7x + 24y + 28 = 0. The area of the square is ______.

To find the area of the square, we first need to find the length of one side. The length of a side of the square can be found by finding the distance between the two parallel lines given by the equations.

The distance d between two parallel lines given by the equations ax + by + c1 = 0 and ax + by + c2 = 0 is given by the formula:

d = |c1 - c2| / sqrt(a^2 + b^2)

Here, a = 7, b = 24, c1 = -72, and c2 = 28.

So, the distance d is:

d = |-72 - 28| / sqrt(7^2 + 24^2) d = 100 / sqrt(49 + 576) d = 100 / sqrt(625) d = 100 / 25 d = 4

Since the square has all sides equal, the length of a side of the square is 4 units.

The area of a square is given by the formula side^2. So, the area of the square is 4^2 = 16 square units.