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.