The side of the square is 3 cm less than one side of the rectangle and 2 cm larger than the other side.

The side of the square is 3 cm less than one side of the rectangle and 2 cm larger than the other side. Find the side of the square if the area of the square is 30cm2 less than the area of the rectangle.

Let the side of the square be x cm, then its area is x ^ 2 cm ^ 2.
Since the side of the square is 3 cm less than one of the sides of the rectangle and 2 cm larger than the other side, then the sides of the rectangle are x + 3 cm and x – 2 cm.Thus, the area of the rectangle is (x + 3) (x – 2) … If the area of the square is 30 cm ^ 2 less than the area of the rectangle, then you can write the equation
(x + 3) (x – 2) – x ^ 2 = 30.
To solve the equation:
– let’s open the brackets
x ^ 2 + 3x – 2x – 6 – x ^ 2 = 30;
– we will give similar
x = 36 (cm) – side of the square.