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

August 24, 2021 | education

| **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.

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