# Perimeter of a Right Triangle

The perimeter of a right triangle is the sum of the lengths of the two legs and the hypotenuse (in other words, the sum of all three sides).

Download this **calculator** to get the results of the formulas on this page. Choose the initial data and enter it in the upper left box. For results, press ENTER.

Triangle-total.rar or Triangle-total.exe

Note. Courtesy of the author: **José María Pareja Marcano**. Chemist. Seville, Spain.

## Exercise: How to Find the Perimeter of a Right Triangle

We can find the perimeter of a right triangle whose sides are *a*=3 cm, *b*=4 cm and *c*=5 cm by adding all the three sides:

The perimeter of the triangle is **12 cm**.

## How do you Find the Perimeter of a Right Triangle using the Pythagorean Theorem?

- If we only know the two legs of the right triangle:
The Pythagorean theorem states that in a right triangle the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two legs.

- If we only know a leg and the hypotenuse of the right triangle we can also find the other leg and the perimeter using the formula that states the Pythagorean theorem:
We just substitute the values and we get the length of the unknown side. Then, we obtain the perimeter by adding the hypotenuse and the two legs of the right triangle.

## How to Find the Perimeter of a Right Triangle using the Leg Rule

The Leg Rule relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.

According to the equation derived from the Leg Rule we can calculate the lengths of the two legs in a right triangle if the hypotenuse and the two projections (*m* and *n*) of the legs (*a* and *b*) on the hypotenuse are given.

So, we get the following formulas for each leg:

If perimeter is equal to *a* + *b* + *c*.

Where *m* and *n* are the segments projected by the legs (*a* and *b*) and *c* is the hypotenuse.

The Leg Rule is useful when the two legs (*a* and *b*) are unknown.