Question

The length of a piece of wire is $78$ m. If the wire is used to make a regular pentagon and a hexagon, find the difference in the lengths of its sides.

Answer 1

If the wire is used to make a regular pentagon

Perimeter of regular pentagon$=78m$

Let the side of regular pentagon be $xm$

Then,$5x=78$

$x=15.6m$

If the wire is used to make regular hexagon

Perimeter of regular hexagon$=78m$

Let the side of regular hexagon be $ym$

Then,$6y=78$

$y=13m$

Therefore difference in the lengths of its sides$=15.6-13=2.6m$