The perimeter of the rectangle is 40 cm. After we reduce its length by 25% and increase its width by 10%

The perimeter of the rectangle is 40 cm. After we reduce its length by 25% and increase its width by 10%, its perimeter is equal to 32.8 cm. Find the lengths of the sides of the first rectangle.

Let’s say that the length of the original rectangle was x cm and the width was y cm. Then its perimeter is:

2 * (x + y) = 40,

x + y = 20,

y = 20 – x.

If the length is reduced by 25%, then it will be:

x * (100 – 25): 100 = 0.75 * x.

If the width is increased by 10%, then it will be:

y * (100 + 10): 100 = 1.1 * y.

The perimeter of the new rectangle is:

2 * (0.75 * x + 1.1 * y) = 32.8,

1.5 * x + 2.2 * (20 – x) = 32.8,

1.5 * x + 44 – 2.2 * x = 32.8,

0.7 * x = 11.2,

x = 16 (cm).

y = 20 – 16 = 4 (cm).