The length of the rectangle was reduced by 15 cm and the width was increased by 5 cm.

| February 3, 2021 | education

The length of the rectangle was reduced by 15 cm and the width was increased by 5 cm. How has the semi-perimeter of the rectangle changed?

Let’s denote the length of this rectangle through a, and the width of this rectangle through b, expressed in centimeters.

Then the semiperimeter p of this rectangle, equal to the sum of its length and width, will be:

p = a + b

If the length of the rectangle is reduced by 15 cm, then the length of the resulting rectangle will be a – 15 cm.

If the width of the rectangle is increased by 5 cm, then the width of the resulting rectangle will be b + 5 cm.

Then the half-perimeter of the resulting rectangle will be a – 15 + b + 5 = a + b – 10 = p – 10 cm.

Therefore, the semi-perimeter of the original rectangle will decrease by 10 cm.

Answer: the semi-perimeter of the original rectangle will decrease by 10 cm.



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