How much is the perimeter of the inner rectangle less than the perimeter of the outer one if the distance

| February 19, 2021 | education

How much is the perimeter of the inner rectangle less than the perimeter of the outer one if the distance between their sides is everywhere 2.5 cm.

Let’s denote the length of the outer rectangular quadrangle by a, and the width of the outer rectangular quadrangle by b.

Then the sum of the lengths of all sides of this quadrangle will be equal to 2a + 2b.

In the initial data for this task, it is reported that each side of the inner rectangle is 2.5 cm from the corresponding side of the outer rectangle, therefore, the length of the inner rectangular quadrangle is a – 2.5 – 2.5 = a – 5 cm, its width is b – 2.5 – 2.5 = b – 5 cm, and the perimeter – 2 * (a – 5) + 2 * (b – 5) = 2a – 10 + 2b – 10 = 2a + 2b – 20 cm.

Consequently, the perimeter of the inner rectangle is two tens of centimeters less than the perimeter of the outer one.

Answer: 20 cm.



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