Question

The perimeter of an equilateral triangle is $ 45{\text{cm}} $ . Find the length of each side of the equilateral triangle.

Answer 1

Hint:
Here we must know that the equilateral triangle is the triangle whose sides are equal. So all the three sides are equal. Perimeter is the sum of all the three sides of the triangle which is given to us as $ 45{\text{cm}} $ so we can easily find the length of each side of this triangle.

Complete step by step solution:
Here we are given that the perimeter of the equilateral triangle is $ 45{\text{cm}} $ and we need to find the length of each side of this triangle. So if we draw the figure of the equilateral triangle:

Here we have assumed that $ ABC $ is an equilateral triangle. We must know that all the sides of an equilateral triangle are equal. So we can say that $ AB = BC = CA $
Perimeter of the triangle is the total length of the boundary of the equilateral triangle. We know that there are three sides of the triangle. The sun of all the three sides of the triangle gives us the perimeter of the triangle.
So we can say that $ AB + BC + CA = {\text{perimeter}} $ $ - - - - - (1) $
We are also given that the perimeter of the given equilateral triangle is $ 45{\text{cm}} $
Hence substituting the value of the perimeter in the given equation:
 $ AB + BC + CA = 45 $ $ - - - (2) $
Now we also know that $ AB = BC = CA $
Let $ AB = BC = CA = x $
Putting this value of $ AB = BC = CA = x $ in equation (2)
 $ x + x + x = 45 $
 $ 3x = 45 $
 $ x = \dfrac{{45}}{3} = 15{\text{cm}} $

So, we get that each side of the triangle $ = x = 15{\text{cm}} $

Note:
Here we must know that the sum of the three sides of the triangle is called the perimeter of the triangle and in the equilateral triangle, three sides are equal in length.