# In a right- angled triangle, the shortest sides are 5 and 12. How do you find the perimeter of the triangle?

The perimeter of the triangle is 30 units.

#### Explanation:

You have to use the "Pythagorean theorem " in order to find the greatest side / Hypotenuse of the triangle .

Pythagorean theorem states that - " The sum of the squares of the smaller sides of a right angled triangle is equal to the square of the greatest side / hypotenuse of right angled triangle ".

Let the third side be 'x'

So ,

${x}^{2} = {5}^{2} + {12}^{2}$

${x}^{2} = 25 + 144$

${x}^{2} = 169$

$x = \sqrt{169}$

$x = 13$

The greatest side / hypotenuse of the triangle = 13

The perimeter of a triangle = Sum of all sides

$= 5 + 12 + 13$

$= 30$