The area of the rectangle is divided into two parts in a ratio of 2: 7.

The area of the rectangle is divided into two parts in a ratio of 2: 7. Calculate the area of each part if the sides of the rectangle are 1 dm and 9 cm.

1) Find the area of the rectangle. The area of a rectangle is equal to the product of its sides S = ab.

1 dm = 10 cm

S = 10 * 9 = 90 (cm ^ 2).

2) Find the area of each part.

Let the area of one part be x cm ^ 2, then the area of the first part is 2x cm ^ 2, and the area of the second part is 7x cm ^ 2. By the condition of the problem, it is known that the area of both parts of the rectangle is (2x + 7x) cm ^ 2 or 90 cm ^ 2. Let’s make an equation and solve it.

2x + 7x = 90;

9x = 90;

x = 90: 9;

x = 10 (cm ^ 2);

2x = 2 * 10 = 20 (cm ^ 2) – the area of the first part;

7x = 7 * 10 = 70 (cm ^ 2) – the area of the second part.

Answer. 20 cm ^ 2, 70 cm ^ 2.