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.