Question

The perimeter of an equilateral polygon-shaped park is $8\text{units}.$ Find the possible length(s) of side of the park (in integer).

• A. 1 units
• B. 2 units
• C. 3 units
• D. 4 units

Answer 1

Answer: (A), (B)

2 units

An equilateral polygon is a polygon that has all the sides of same length.

Let, the length of each side be $a\text{units},$ and there are $n$ sides.

$\text{Perimeter}=\text{Sum of all the sides}$
$\Rightarrow 8\text{units}=n\times a$
where, both $n$ and $a$ are integers.

$a\times n$	$=8$
$1\times 8$ $2\times 4$ $4\times 2$	$=8$ $=8$ $=8$

However, $n\ge 3$ as a triangle is the smallest possible polygon according to number of sides.

Here, possible values of $n$ are $8$ and $4,$ corresponding to side lengths $1\text{unit}$ and $2\text{units},$ respectively.