# Perimeter of a Triangle

The length of boundary of a triangle is defined perimeter of a triangle.

The boundary of a triangle is the perimeter of a triangle but its boundary is formed by three line segments. Therefore, the boundary of a triangle is equal to the total of lengths of all three sides.

## Example

Consider triangle $XYZ$. It is having sides $\stackrel{‾}{XY}$, $\stackrel{‾}{YZ}$ and $\stackrel{‾}{ZX}$, and their lengths are $XY$, $YZ$ and $ZX$ respectively. Perimeter of a triangle is the total of lengths of all three sides. So, it can be expressed in a mathematical form.

### Formula

Perimeter of Triangle = Length of First Side + Length of Second Side + Length of Third Side

According to $\Delta XYZ$,

1. Length of the side $\stackrel{‾}{XY}$ is $XY=10cm$
2. Length of the side $\stackrel{‾}{YZ}$ is $YZ=12cm$
3. Length of the side $\stackrel{‾}{ZX}$ is $ZX=6cm$

Perimeter of the triangle $XYZ$ can be calculated now by substituting the lengths of the sides in the above formula.

Perimeter of $\Delta XYZ$ $=$ Length of the side $\stackrel{‾}{XY}$ $+$ Length of the side $\stackrel{‾}{YZ}$ $+$ Length of the side $\stackrel{‾}{ZX}$

Perimeter of $\Delta XYZ$ $=$ $XY$ $+$ $YZ$ $+$ $ZX$

Perimeter of $\Delta XYZ$ $=$ $10$ $+$ $12$ $+$ $6$

Perimeter of $\Delta XYZ$ $=$ $28$

Therefore, the perimeter of the triangle $XYZ$ is $28cm$. Use this method to calculate the perimeter of any triangle in mathematical system.

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