The perimeter of the rectangle is 40 cm If its length is reduced by 20% and the width is increased by 20%

The perimeter of the rectangle is 40 cm If its length is reduced by 20% and the width is increased by 20%, then the perimeter will be 36 cm. Find the original length and width of the rectangle.

1. Take the initial length of the larger side of the rectangle as x, and the initial length of the smaller side as y.

2. Let’s compose two equations:

2x + 2y = 40;

2 (x – 0.2x) + 2 (y + 0.2y) = 36; 2x – 0.4x + 2y + 0.4y = 36; 1.6x + 2.4y = 36; x = (36 -, 4y) / 1.6;

3. Substitute x = (36 – 2.4y) / 1.6 into the first equation:

2 (36 – 2.4y) / 1.6 + 2y = 40;

45 – 3y + 2y = 40;

-y = – 5;

y = 5 cm.

2x + 10 = 40;

x = 15 cm.

Answer: the initial length of the larger side of the rectangle is 15 cm, the initial length is less than 5 cm.