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).

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.