The side of the square is 2 cm larger than one of the sides of the rectangle and 5 cm smaller than the other.

The side of the square is 2 cm larger than one of the sides of the rectangle and 5 cm smaller than the other. Find the area of the square if it is known that it is 50cm2 less than the area of the rectangle.

Let the side of the square be x cm, then one of the sides of the rectangle is (x – 2) cm, and the second side of the rectangle is (x + 5) cm. The area of ​​the square is equal to the square of its side, i.e. x ^ 2 ci ^ 2. The area of ​​a rectangle is equal to the product of its sides, i.e. (x – 2) (x + 5) cm ^ 2. By the condition of the problem, it is known that the area of ​​a square is less than the area of ​​a rectangle by ((x – 2) (x + 5) – x ^ 2) cm ^ 2 or by 50 cm ^ 2. Let’s make an equation and solve it.

(x – 2) (x + 5) – x ^ 2 = 50;

x ^ 2 + 5x – 2x – 10 – x ^ 2 = 50;

3x – 10 = 50;

3x = 50 + 10;

3x = 60;

x = 60: 3;

x = 20 (cm) – side of the square.

Find the area of ​​the square.

20 ^ 2 = 400 (cm ^ 2).

Answer. 400 cm ^ 2.