Question

two people describe a regular polygon. Brianna says that the polygon has side length 6.3cm and a perimeter 31.5cm. Desiderio says the polygon has side length n and perimeter 5n. which person's description tells you how many sides the polygon has without doing any calculations? why?​

Answer 1

9514 1404 393

Answer:

Desiderio

Explanation:

The number of sides of a regular polygon is multiplied by the length of the side to get the perimeter. To find the number of sides, the perimeter must be divided by the number of sides.

Brianna's description requires that division look like ...

31.5/6.3 = 5

Desiderio's description requires that division look like ...

5n/n = 5

Since we're supposed to tell the number of sides without doing any calculation, it seems Desiderio's description is better. (We have to realize that n/n = 1, so the factors of n cancel.)

Some of us are familiar with multiplication tables and quickly realize 30/6 = 5 based on memory. Which realization is faster depends on your memory and experience. Most would say evaluating Brianna's description cannot be done without calculation.