Question

The length of each side of an equilateral triangle is increased by $5$ inches, so, the perimeter is now $60$inches. How do you write and solve an equation to find the original length of each side of the equilateral triangle?

Answer 1

Hint: We know that the length of each side of an equilateral triangle is equal and we also know that the sum of all the sides of a triangle is its perimeter. Now, in this question there is a statement given which we have to convert in an equation to find the length of the side.

Complete step by step answer:

In the above question, it is given that the triangle is an equilateral triangle. Therefore, the length of all sides of the triangle is equal.
Now, let the length of each side of the triangle be x.
Now, it is given that if the length of each side of an equilateral triangle is increased by $5$ inches, so, the perimeter is now $60$inches.
Therefore, in equation form we can write it as
$x + 5 + x + 5 + x + 5 = 60$
now adding all the constant terms and variable terms in LHS.
$3x + 15 = 60$
Now taking $3$as common from LHS
$3\left( {x + 5} \right) = 60$
Now divide both sides by $3$, we get
$x + 5 = 20$
Now, transposing $5$ to the right-hand side.
$x = 20 - 5$
$x = \,15\,inches$

Note:
In this question we have found the length of an equilateral triangle. Now, we can find the area of the equilateral triangle of new length as well as of the previous length. The increment in the area of the triangle is directly proportional to square of side whereas it is linearly proportional in increment of perimeter.