The length of the side of the rectangle is 2cm. What should be the length of the other side so that the perimeter

The length of the side of the rectangle is 2cm. What should be the length of the other side so that the perimeter of the rectangle is less than or equal to the perimeter of an equilateral triangle with a side of 6cm.

First, let’s find what the sum of the lengths of all three sides of an equilateral triangle with a side length of six centimeters is equal to:

6 + 6 + 6 = 12 + 6 = 18 cm.

Let x denote the side length of this rectangular quadrangle.

In order for the sum of the lengths of all four sides of a given quadrangle to be less than or equal to 18 cm, it is necessary that the following inequality holds:

x + 2 + x + 2 <= 18.

Let us find at what values ​​of x this inequality is satisfied:

2x + 4 <= 18;

(2x + 4) / 2 <= 18/2;

x + 2 <= 9;

x <= 9 – 2;

x <= 7.

Therefore, the length of the other side must be less than or equal to seven centimeters.

Answer: the length of the other side must be less than or equal to 7 cm.