The width of the rectangle was increased by 3 cm and a square was obtained, the area of which is 24 cm2

The width of the rectangle was increased by 3 cm and a square was obtained, the area of which is 24 cm2 larger than the area of the rectangle. Find the perimeter of the rectangle?

Let’s denote by x the length of the given 4-gon, all four angles of which are 90 degrees, and by y – its width.

Then the area of ​​this geometric figure will be x * y cm².

In the initial data for this task, it is reported that after increasing the width by 3 cm, the area of ​​the resulting square turned out to be 24 cm² larger than the area of ​​the original quadrilateral, therefore, the following ratios take place:

y = x + 3;

y² = 24 + xy.

We solve the resulting system of equations.

Substituting into the second equation the value y = x + 3 from the first equation, we get:

(x + 3) ² = 24 + x * (x + 3);

x² + 6x + 9 = 24 + x² + 3x;

6x – 3x = 24 – 9;

3x = 15;

x = 15/3 = 5 cm.

We find at:

y = x + 3 = 5 + 3 = 8 cm.

Find the sum of the lengths of all four sides of the original quadrilateral:

5 + 8 + 5 + 8 = 13 + 13 = 26 cm.

Answer: 26 cm.