The length of the rectangle has been reduced by 10% and the width has been reduced by 30%. In this case

The length of the rectangle has been reduced by 10% and the width has been reduced by 30%. In this case, the perimeter of the rectangle decreased by 18%. By what percentage will the perimeter of a rectangle decrease if its length is reduced by 30% and its width is reduced by 10%?

The perimeter of the rectangle is equal to twice the sum of the length a and the width c:

P = 2 (a + c).

If the length of the rectangle was reduced by 10% (0.9a), and the width – by 30% (0.7c), then the perimeter decreased by 18%:

0.82P = 2 (0.9a + 0.7s).

If the length is reduced by 30% (0.7a), and the width is reduced by 10% (0.9c), then the perimeter will be

xP = 2 (0.7a + 0.9c).

To calculate x, it is necessary in the last two equations to open the brackets and sum

(0.82 + x) P = 1.6 * 2 (a + c).

Whence, 0.82 + x = 1.6 and x = 0.78, then the perimeter will decrease by 22%.