The perimeter of the rectangle is 14 cm, and its area is 12 cm square. What are the sides of the rectangle.

We know two quantities – the perimeter and the area of the rectangle.

These values are related by the fact that only the length and width of the rectangle are needed to find them.

Let’s introduce two variables.

Let x be the length of the rectangle, then y is its width.

Perimeter is twice the sum of the length and width of the rectangle. The area is their product. We get two equations:

(x + y) * 2 = 14; y = 7 – x;

x * y = 12;

We get:

x * (7 – x) = 12;

7 * x – x ^ 2 – 12 = 0;

x ^ 2 – 7 * x + 12 = 0;

D = 49 – 48 = 1;

x1 = (7 – 1) / 2 = 3;

x2 = (7 + 1) / 2 = 4;

If x = 3, then y = 4;

If x = 4, then y = 3.

The pair (4; 3) is suitable for us, since the length is greater than the width.