# One side of the rectangle is 2 cm larger than the other. If one side of the rectangle is increased by 2 times

**One side of the rectangle is 2 cm larger than the other. If one side of the rectangle is increased by 2 times and the other by 3 cm, then the perimeter of the new rectangle will be 28 cm. Find the sides of the rectangle.**

Let’s denote by x the length of the shorter side of this rectangle.

According to the condition of the problem, one side of this rectangle is 2 cm larger than the other, therefore, the length of the larger side of this rectangle is x + 2 cm.

According to the condition of the problem, if one side of the rectangle is increased by 2 times, and the other by 3 cm, then the perimeter of the new rectangle will be 28 cm.

Let’s consider 2 cases.

1) If the smaller side of the rectangle is doubled, and the larger side is increased by 3 cm, and the perimeter of the new rectangle is 28 cm, we can write the following equation:

2 * (2 * x + x + 2 + 3) = 28.

We solve the resulting equation:

2 * (3 * x + 5) = 28;

3 * x + 5 = 28/2;

3 * x + 5 = 14;

3 * x = 14 – 5;

3 * x = 9;

x = 9/3;

x = 3 cm.

Knowing the length of the smaller side, we find the length of the larger side:

x + 2 = 3 + 2 = 5 cm.

1) If the large side of the rectangle is doubled, and the smaller side is increased by 3 cm, and the perimeter of the new rectangle is 28 cm, we can write the following equation:

2 * (x + 3 + 2 * (x + 2)) = 28.

We solve the resulting equation:

2 * (x + 3 + 2 * x + 4) = 28;

2 * (3 * x + 7) = 28;

3 * x + 7 = 28/2;

3 * x + 7 = 14;

3 * x = 14 – 7;

3 * x = 7;

x = 7/3 cm = 2 1/3 cm.

Knowing the length of the smaller side, we find the length of the larger side:

x + 2 = 7/3 + 2 = 13/3 = 4 1/3 cm.

Answer: the condition of the problem is satisfied by two rectangles with sides of 3 cm and 5 cm and sides of 2 1/3 cm and 4 1/3 cm.