Question

The perimeter of an equilateral triangle is $16.5\,cm$ . Find the length of its side. (in cm)

Answer 1

Hint: In this question we need to find the length of each side of an equilateral triangle. We know that all the sides of an equilateral triangle are equal. So we will assume the length of the side of an equilateral triangle is $x$ cm. After this we will use the formula of perimeter of an equilateral triangle to solve this question.

Complete step by step answer:
We know that an equilateral triangle is a triangle in which the length of all three sides is equal and all the angles are also equal i.e. $60^\circ $.Let us assume that the side of an equilateral triangle is $x$.We can also draw the diagram representing the given data in the question i.e.

In the above image, ABC is an equilateral triangle. And all the sides and angles are equal:
$AB = BC = AC = x\,cm$
And, $\angle A = \angle B = \angle C = 60^\circ $.
Now we know that the perimeter of an equilateral triangle is equal to the sum of the length of its three sides. Or we can say the formula of perimeter of an equilateral triangle is $3a$ , where $a$ is the length of each side.
Here we have $a = x$ .
Now by putting values we can write:
$x + x + x = 16.5$
Or, by applying formula it can be written as
$3x = 16.5$
On simplifying we have
$x = \dfrac{{16.5}}{3} \\
\therefore x= 5.5\,cm$

Hence the required length of the side of an equilateral triangle is $5.5\,cm$.

Note:We should always remember the formula to help in easy calculation. The formula for the area of an equilateral triangle is $\dfrac{{\sqrt 3 }}{4}{a^2}$. We can calculate the semi perimeter of an equilateral triangle by the formula:$\dfrac{{3a}}{2}$ , where $a$ is the length of the side of an equilateral triangle.Similarly we can calculate the height of an equilateral with formula:$\dfrac{{\sqrt 3 }}{2}a$.