Question

How do you calculate the perimeter of an isosceles triangle?

Answer 1

Hint: An isosceles triangle is one of the triangles that has two of its sides of equal length. Generally, it is explained as having exactly two sides of equal length but sometimes it is explained as having at least two of its sides of equal length. In the latter case, the equilateral triangle becomes a special case as it has all of its three sides equal in length.
Moreover, the perimeter is the distance around a regular polygon or a 2d shape. We can find the perimeter of a regular polygon by just simply adding all of its side lengths.

Complete step by step solution:

Let there be an isosceles triangle $\Delta ABC$ whose two sides $AB$ and $CB$ are equal. Hence $AB = CB$.
Also, let $AB = CB = a$(say) and $AC = b$(say).
So, the perimeter of $\Delta ABC$
$ = AB + CB + AC$ (Since perimeter is the sum of all the side lengths)
On substituting the values of $AB$, $CB$, and $AC$, we get
$ = a + a + b$
$ = 2a + b$
So, the perimeter of $\Delta ABC$ is $2a + b$.

Hence, the perimeter of an isosceles triangle is the sum of twice its one of the equal side and the unequal side.

Note:
The two equal sides of an isosceles triangle are defined as the legs of the triangle whereas the unequal side or the third side is defined as the base of the triangle. Also in an isosceles triangle, the angles opposite the equal sides are also equal in measurement.