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.

Consider triangle

$XYZ$. It is having sides

$\stackrel{\u203e}{XY}$,

$\stackrel{\u203e}{YZ}$and

$\stackrel{\u203e}{ZX}$, 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.

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

According to

$\Delta XYZ$,

- Length of the side

$\stackrel{\u203e}{XY}$is

$XY=10cm$ - Length of the side

$\stackrel{\u203e}{YZ}$is

$YZ=12cm$ - Length of the side

$\stackrel{\u203e}{ZX}$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

$\stackrel{\u203e}{XY}$ $+$Length of the side

$\stackrel{\u203e}{YZ}$ $+$Length of the side

$\stackrel{\u203e}{ZX}$$\Rightarrow $

Perimeter of

$\Delta XYZ$ $=$ $XY$ $+$ $YZ$ $+$ $ZX$$\Rightarrow $

Perimeter of

$\Delta XYZ$ $=$ $10$ $+$ $12$ $+$ $6$$\Rightarrow $

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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