One of the sides of the rectangle is 2 cm larger than the other side, and the area of the rectangle

One of the sides of the rectangle is 2 cm larger than the other side, and the area of the rectangle does not exceed 15 cm2. What values can the perimeter of a rectangle take?

One side of the rectangle is 2 cm larger than the other.

The area of ​​the rectangle does not exceed 15 cm². Let’s find the possible values ​​for the perimeter of the rectangle.

The area of ​​a rectangle is the product of length and height.

Let’s introduce a variable. Let x be the width of the rectangle, then (x + 2) is its length. Based on the conditions of the problem, we compose and solve the inequality:

x * (x + 2) <= 15;

x ^ 2 + 2 * x – 15 <= 0;

x ^ 2 + 2 * x + 1 – 16 <= 0;

(x + 1) ^ 2 <= 16;

-4 <= x + 1 <= 4;

-5 <= x <= 3.

If we take whole values ​​of the width, then it can be equal to 1, 2 or 3 cm.

If x = 1, then P = 2 * (1 + 3) = 8 cm.

If x = 2, then P = 2 * (2 + 4) = 12 cm.

If x = 3, then P = 2 * (3 + 5) = 16 cm.