Question

A regular pentagon of each side 12 cm has the same perimeter as that of a regular hexagon. Find the length (in cm) of each side of the hexagon.

Answer 1

Hint: First of all, find the perimeter of the given regular pentagon. Consider the side of the regular hexagon as a variable and find its perimeter. Then equate both the perimeters to find the side of the regular hexagon.

Complete step-by-step answer:

Given length of side of a regular pentagon is 12 cm

We know that the perimeter of a regular pentagon of side length \[a\] is given by \[5a\].

So, perimeter of the given regular pentagon \[ = 5 \times 12 = 60\]

Let the length of the regular hexagon is \[b{\text{ cm}}\]

We know that the perimeter of a regular hexagon of side length \[b\] is given by \[6b\].

So, the perimeter of the given regular hexagon \[ = 6 \times b\]

Given that the perimeter of the regular pentagon and regular hexagon are equal, we have

\[

   \Rightarrow 60 = 6b \\

   \Rightarrow b = \dfrac{{60}}{6} \\

  \therefore b = 10{\text{ cm}} \\

\]

Thus, the side of the regular hexagon is 10 cm.

Note: The perimeter of a regular pentagon of side length \[a\] is given by \[5a\]. The perimeter of the regular hexagon of side length \[b\] is given by \[6b\]. The length of the side of the given regular hexagon cannot be negative.