The perimeter of the rectangle is 65cm. If the length of the rectangle is reduced by 6 cm and the width is increased

The perimeter of the rectangle is 65cm. If the length of the rectangle is reduced by 6 cm and the width is increased by 2 cm, then its area will decrease by 27 cm2. Find the area of the rectangle.

Let us denote the lengths of the sides of this rectangular quadrangle by x and y.

In the initial data for this task, it is reported that the sum of the lengths of all four sides of this quadrangle is 65 cm, therefore, the following relationship holds:

2x + 2y = 65.

It is also known that if the length of a rectangular quadrangle
decrease by 6 cm, and increase the width by 2 cm, then its area will decrease by 27 cm², therefore, the following relationship holds:

(x – 6) * (y + 2) = xy – 27.

Simplifying this ratio, we get:

xy + 2x – 6y – 12 = xy – 27;

2x – 6y = 12 – 27;

2x – 6y = -15.

Subtracting the resulting ratio from the first equation, we get:

2x + 2y – 2x + 6y = 65 + 15;

8y = 80;

y = 80/8 = 10 cm.

Find x:

x = 32.5 – y = 32.5 – 10 = 22.5 cm.

We find the area of ​​this geometric figure:

10 * 22.5 = 225 cm².

Answer: 225 cm².