# If the length of the rectangle is reduced by 2 cm, and the width is increased by 1 cm

**If the length of the rectangle is reduced by 2 cm, and the width is increased by 1 cm, you will get a square whose area is 4 cm2 less than the area and the rectangle. Find the side of the square.**

Take the side of the square as a.

Then the length of the rectangle (x) is equal to a + 2.

The width of the rectangle (y) is a-1.

The area of the square is 4 cm2 less than the area of the rectangle.

S square = a2.

S of rectangle = x * y.

Let’s make the equation:

a2 + 4 = x * y.

a2 + 4 = (a + 2) (a-1).

a2 + 4 = a2 + 2a-a-2.

a2 + 4 = a2 + a-2.

a2-a2 + a = 4 + 2 = 6.

a = 6 cm2 – side of the square.

a + 2 = 6 + 2 = 8 cm2 – the length of the rectangle.

a-1 = 6-1 = 5 cm2 – the width of the rectangle.

Verification:

6 * 6 + 4 = 8 * 5

40 = 40.

Answer: the side of the square is 6 cm.