The side of the square is equal to the width of the rectangle. The length of the rectangle is 2 times its width

The side of the square is equal to the width of the rectangle. The length of the rectangle is 2 times its width. Calculate the side of a square if its perimeter is 14 cm less than the perimeter of the rectangle.

Let the side of the square be x cm, then the width of the rectangle is also x cm, since it is known from the condition of the problem that the side of the square is equal to the width of the rectangle.

2 ∙ х (cm) – the length of the rectangle, since it is 2 times its width;

4 ∙ х (cm) – perimeter of the square;

2 ∙ (x + 2 ∙ x) (cm) – the perimeter of the rectangle.

Knowing that the perimeter of the square is 14 cm less than the perimeter of the rectangle, we compose the equation:

4 ∙ x + 14 = 2 ∙ (x + 2 ∙ x);

4 ∙ x + 14 = 6 ∙ x;

6 ∙ x – 4 ∙ x = 14;

2 ∙ x = 14;

x = 7 (cm) – side of the square.

Answer: 7 cm is the side of the square.