how to find the perimeter of a triangle

The perimeter of a right triangle is the total length effectually the triangle. Nosotros can detect the perimeter by adding the lengths of all the sides of the triangle. Since we can utilise the Pythagorean theorem to find the length of a third side if we know the lengths of two sides of the triangle, we but need the length of 2 sides of the triangle.

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

GEOMETRY

formula for the perimeter of a right triangle

Relevant for…

Learning near the perimeter of a right triangle with examples.

See examples

GEOMETRY

Relevant for…

Learning nearly the perimeter of a right triangle with examples.

See examples

Formula for the perimeter of an equilateral triangle

Nosotros can find the perimeter of a right triangle by calculation the lengths of all the sides of the triangle. Therefore, nosotros can use the following formula:

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

If nosotros know the lengths of 2 sides, we tin can utilise the Pythagorean theorem to detect the length of the tertiary 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:

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

Perimeter of a right triangle – Examples with answers

With the post-obit examples, you can practise solving problems related to correct triangles. Each example has its corresponding solution and reasoning.

EXAMPLE one

What is the perimeter of a triangle that has sides of length viii k, 9 one thousand, and 12.4 chiliad?

Solution

We can place the following values:

Using the perimeter formula, we have:

$p=a+b+c$

$p=8+9+12.4$

$p=29.4$

The perimeter is 29.iv m.

EXAMPLE 2

Nosotros have an equilateral triangle with sides of length ten m, 24 grand, and 26 g. What is the perimeter?

Solution

We have the following:

Using the perimeter formula, we accept:

$p=a+b+c$

$p=10+24+26$

$p=60$

The perimeter is 60 g.

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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:

We supervene upon these values in the perimeter formula:

$p=a+b+c$

$p=11+12+16.28$

$p=39.28$

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 accept the following sides:

We take to find the length of the 3rd side. Therefore, we starting time by using the Pythagorean theorem:

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

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

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

${{c}^2}=169$

$c=13$

Now, we tin employ the perimeter formula with these lengths:

$p=a+b+c$

$p=5+12+13$

$p=30$

The perimeter is 30 1000.

Case 5

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

Solution

We accept the post-obit lengths:

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

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

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

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

${{c}^2}=185$

$c=13.6$

We use these lengths to find the perimeter:

$p=a+b+c$

$p=8+11+13.6$

$p=32.6$

The perimeter is 32.6 m.

Perimeter of a right triangle – Practise problems

Put into do what you take learned about the perimeter of correct triangles and the Pythagorean theorem to solve the following problems. If you demand aid with these problems, you can await at the solved examples above.