Construct an equilateral triangle, given its side = 3 and justify its construction.

Hint: In this particular question use the concept that if all the sides of a triangle are equal than it is an equilateral triangle and in an equilateral triangle all angles are equal to 60 degrees so first draw a line of 3 cm using a ruler then construct the angle of 60 degrees from both the end of this line, so use these concepts to reach the solutions of the questions.

Complete step-by-step answer:
Steps of construction
$\left( i \right)$ Draw of line BC of 3 cm using a ruler as shown in the below figure.

$\left( {ii} \right)$ Now make an arc from both the ends of the line using the compass with pointed end of the compass on point B and C respectively and make an arc with the pencil end as shown below which cut the line BC at point D and E respectively. Consider an appropriate distance in the compass less than half of the distance of the line BC.

$\left( {iii} \right)$ Now with the same distance in the compass mark an arc from point D and E on the previous arcs which cut the arcs at point F and G as shown below.

$\left( {iv} \right)$ Now join points B to F and C to G and extend further so that both the lines cut at the point A, as shown in the below figure.

So ABC is the required equilateral triangle of side 3 cm.
Now as we measure the sides from the ruler we get AB = BC = CA = 3cm.
So we can say this is an equilateral triangle.
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall the steps of construction which is stated above, these steps are the basis of the construction, without these steps we cannot draw the equilateral triangle of side 3 cm.