The perimeter of a right triangle is the total length around the triangle. We can find the perimeter by adding the lengths of all the sides of the triangle. Since we can use the Pythagorean theorem to find the length of a third side if we know the lengths of two sides of the triangle, we simply need the length of two sides of the triangle.

Here, we will learn about the formula for the perimeter of a right triangle. Also, we will do a review of the Pythagorean theorem that we can use to calculate the lengths of the sides. Finally, we will see some examples in which we will apply the learned formulas.

## Formula for the perimeter of an equilateral triangle

We can find the perimeter of a right triangle by adding the lengths of all the sides of the triangle. Therefore, we can use the following formula:

$latex p=a+b+c$ |

where, $latex a, ~ b, ~ c$ are the lengths of the sides of the triangle.

If we know the lengths of two sides, we can use the Pythagorean theorem to find the length of the third side and at the same time find the perimeter. Recall that the Pythagorean theorem tells us that the square of the hypotenuse is equal to the sum of the squares of the other sides:

$latex {{c}^2}={{a}^2}+{{b}^2}$

## Perimeter of a right triangle – Examples with answers

With the following examples, you can practice solving problems related to right triangles. Each example has its respective solution and reasoning.

**EXAMPLE 1**

What is the perimeter of a triangle that has sides of length 8 m, 9 m, and 12.4 m?

##### Solution

We can identify the following values:

- Side 1, $latex a=8$ m
- Side 2, $latex b=9$ m
- Side 3, $latex c=12.4$ m

Using the perimeter formula, we have:

$latex p=a+b+c$

$latex p=8+9+12.4$

$latex p=29.4$

The perimeter is 29.4 m.

**EXAMPLE 2**

We have an equilateral triangle with sides of length 10 m, 24 m, and 26 m. What is the perimeter?

##### Solution

We have the following:

- Side 1, $latex a=10$ m
- Side 2, $latex b=24$ m
- Side 3, $latex c=26$ m

Using the perimeter formula, we have:

$latex p=a+b+c$

$latex p=10+24+26$

$latex p=60$

The perimeter is 60 m.

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**EXAMPLE 3**

What is the perimeter of a right triangle that has sides of length 11 cm, 12 cm, and 16.28 cm?

##### Solution

We have the following lengths:

- Side 1, $latex a=11$ cm
- Side 2, $latex b=12$ cm
- Side 3, $latex c=16.28$ cm

We replace these values in the perimeter formula:

$latex p=a+b+c$

$latex p=11+12+16.28$

$latex p=39.28$

The perimeter is 39.28 cm.

**EXAMPLE 4**

What is the perimeter of a right triangle that has sides of length 5 m and 12 m?

##### Solution

We have the following sides:

- Side 1, $latex a=5$ m
- Side 2, $latex b=12$ m

We have to find the length of the third side. Therefore, we start by using the Pythagorean theorem:

$latex {{c}^2}={{a}^2}+{{b}^2}$

$latex {{c}^2}={{5}^2}+{{12}^2}$

$latex {{c}^2}=25+144$

$latex {{c}^2}=169$

$latex c=13$

Now, we can use the perimeter formula with these lengths:

$latex p=a+b+c$

$latex p=5+12+13$

$latex p=30$

The perimeter is 30 m.

**EXAMPLE 5**

A right triangle has sides of lengths 8 m and 11 m. What is the perimeter?

##### Solution

We have the following lengths:

- Side 1, $latex a=8$ m
- Side 2, $latex b=11$ m

We can use the Pythagorean theorem to find the length of the third side:

$latex {{c}^2}={{a}^2}+{{b}^2}$

$latex {{c}^2}={{8}^2}+{{11}^2}$

$latex {{c}^2}=64+121$

$latex {{c}^2}=185$

$latex c=13.6$

We use these lengths to find the perimeter:

$latex p=a+b+c$

$latex p=8+11+13.6$

$latex p=32.6$

The perimeter is 32.6 m.

## Perimeter of a right triangle – Practice problems

Put into practice what you have learned about the perimeter of right triangles and the Pythagorean theorem to solve the following problems. If you need help with these problems, you can look at the solved examples above.

## See also

Interested in learning more about right triangles? Take a look at these pages:

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