The perimeter of the rectangle is 22 dm. Find the sum of the lengths of the distances from any

| September 8, 2021 | education

The perimeter of the rectangle is 22 dm. Find the sum of the lengths of the distances from any inner point of the rectangle to its sides.

Let’s denote the length of this rectangle by a, and the width of this rectangle by b.

Select any point within this rectangle.

Then the sum of the distances from this point to two opposite sides of the rectangle, which are its length, will be b dm, and the sum of the distances from this point to two opposite sides of the rectangle, which are its width, will be a dm.

Therefore, the sum of the lengths of the distances from this point to all four sides of the rectangle will be a + b dm.

According to the condition of the problem, the perimeter of the rectangle is 22 dm.

Therefore, the following relation holds:

2 * (a + b) = 22,

whence it follows that a + b = 22/2 = 11 dm.

Answer: the required value is 11 dm.



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