# The difference between the two sides of the rectangle = 7cm, and its perimeter is 54cm. Find the sides of the rectangle.

Let’s denote the length of this rectangular quadrangle by x, and the width of this rectangular quadrilateral by y.

In the initial data for this task, it is reported that if you subtract its width from the length of a given rectangular quadrilateral, then the result will be 7 cm, therefore, the following relationship holds:

x – y = 7.

It is also known that the perimeter of this geometric figure is 54 cm, therefore, the following relationship takes place:

2x + 2y = 54.

We solve the resulting system of equations.

Substituting into the second equation the value x = 7 + y from the first equation, we get:

2 * (7 + y) + 2y = 54;

14 + 2y + 2y = 54;

14 + 4y = 54;

4y = 54 – 14;

4y = 40;

y = 40/4 = 10 cm.

Find x:

x = 7 + y = 7 + 10 = 17 cm.

Answer: 10 cm and 17 cm.

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