Question

A wire $1m68cm$long is cut into two equal pieces . One piece is used to make a regular hexagon and the other is used to make a regular pentagon . Find the difference is the sides of the pentagon and hexagon formed.

Answer 1

Step 1: Finding length of each piece of wire

Converting $m$into $cm$

$$\begin{gathered} 1m=100cm \\ 1m68cm=168cm \end{gathered}$$

Total length of wire $=168cm$

Length of each piece $$\begin{gathered} =\frac{168}{2} \\ =84cm \end{gathered}$$

Step 2: Finding side of regular hexagon :

Perimeter of regular hexagon $=6\times side$

$$\begin{gathered} 84=6\times side \\ side=\frac{84}{6} \\ side=14cm \end{gathered}$$

Step 3: Finding side of regular pentagon :

Perimeter of regular pentagon $=5\times side$

$$\begin{gathered} 84=5\times side \\ side=\frac{84}{5} \\ side=16.8cm \end{gathered}$$

Step 4: Finding the difference between sides :

Difference between sides $$\begin{gathered} =16.8-14 \\ =2.8cm \end{gathered}$$

Hence, the difference between sides is $2.8cm$