Question

The perimeter of an equilateral triangle is 45 cm. Find the length of each side of the equilateral triangle.

Answer 1

Hint:
Here, we need to find the length of each side of the equilateral triangle. Let the length of each side of the equilateral triangle be \[k\] cm. We will use the formula for the perimeter of a triangle to form a linear equation in terms of \[k\]. Then, we will solve this linear equation to obtain the value of \[k\], and hence, the length of each side of the equilateral triangle.

Complete step by step solution:
Let the length of each side of the equilateral triangle be \[k\] cm.
Now, we know that the perimeter of a triangle is equal to the sum of the lengths of the three sides.
The perimeter of an equilateral triangle is the sum of its three equal sides.
Therefore, we get
Perimeter of the given equilateral triangle \[ = k + k + k\]
It is given that the perimeter of the equilateral triangle is 45 cm.
Therefore, we get the equation
\[ \Rightarrow k + k + k = 45\]
This is a linear equation in terms of \[k\]. We will solve this equation to find the value of \[k\].
Adding the like terms, we get
\[ \Rightarrow 3k = 45\]
Dividing both sides by 3, we get
\[ \Rightarrow k = \dfrac{{45}}{3}\]
Simplifying the expression, we get
\[ \Rightarrow k = 15\]
Thus, we get the value of \[k\] as 15.

\[\therefore \] The length of each side of the given equilateral triangle is 15 cm.

Note:
We have formed a linear equation in one variable in terms of \[k\] in the solution. A linear equation in one variable is an equation of the form \[ax + b = 0\], where \[a\] and \[b\] are integers and have only one solution.
The given triangle is an equilateral triangle. An equilateral triangle is a triangle in which the length of all the three sides is equal and has an equal angle of \[60^\circ \].