115 LearnersLast updated on August 5th, 2025
Perimeter of Right Triangle
The perimeter of a shape is the total length of its boundary. For a right triangle, the sum of all three sides is called the perimeter. Perimeter calculations are useful in various practical applications such as construction, art, and design. In this topic, we will learn about the perimeter of a right triangle.
What is the Perimeter of a Right Triangle?
The perimeter of a right triangle is the total length of its three sides, including the two legs and the hypotenuse. By adding the lengths of all three sides, we get the perimeter of the shape. The formula for the perimeter of a right triangle is 𝑃 = 𝑎 + 𝑏 + 𝑐, where a and b are the legs and c is the hypotenuse. For instance, if a right triangle has legs a = 3, b = 4, and hypotenuse c = 5, then its perimeter is P = 3 + 4 + 5 = 12.
Formula for Perimeter of Right Triangle - 𝑃 = 𝑎 + 𝑏 + 𝑐.
Let’s consider another example of a right triangle with side lengths 𝑎 = 5, 𝑏 = 12, and 𝑐 = 13. So the perimeter of the right triangle will be: 𝑃 = 𝑎 + 𝑏 + 𝑐 = 5 + 12 + 13 = 30.
How to Calculate the Perimeter of a Right Triangle
To find the perimeter of a right triangle, apply the formula by summing all the sides of the triangle. For instance, for a right triangle with sides a = 6, b = 8, and c = 10, the perimeter = sum of all sides = 6 + 8 + 10 = 24 cm. Example Problem on Perimeter of Right Triangle - To find the perimeter of a right triangle, use the formula, 𝑃 = 𝑎 + 𝑏 + 𝑐. For example, let’s say, a = 9 cm, b = 12 cm, and c = 15 cm. Now, the perimeter = sum of all sides = 9 + 12 + 15 = 36 cm. Therefore, the perimeter of the right triangle is 36 cm.
Tips and Tricks for Perimeter of Right Triangle
Learning some tips and tricks makes it easier to calculate the perimeter of right triangles. Here are some tips and tricks: Always remember that a right triangle's perimeter is the sum of its three sides. Use the formula, 𝑃 = 𝑎 + 𝑏 + 𝑐. When calculating the perimeter, determine each side length using known properties or measurements. For a right triangle, if two sides are known, the Pythagorean theorem can be used to find the third side if needed. Organize your side lengths clearly, especially when dealing with multiple triangles, to avoid confusion. Apply the formula to each triangle as needed. Ensure side lengths are precise and consistent, especially for practical applications like construction or design. If you have the semi-perimeter, which is half the perimeter, you can multiply it by 2 to find the full perimeter. This can be useful in certain calculations, like using Heron's formula for area.
Common Mistakes and How to Avoid Them in Perimeter of Right Triangle
While working with the perimeter of a right triangle, errors can occur. Here are solutions to common problems:
Mistake 1
Incorrectly applying the Pythagorean theorem (a² + b² = c²) to identify non-right triangles.
Remember that the Pythagorean theorem applies only to right-angled triangles. Sum the lengths of all sides to find the perimeter.
Mistake 2
Confusion between area and perimeter, leading to miscalculations.
It is important to note that the perimeter, measured in linear units, is the total length of the triangle’s sides, while the area, in square units, represents the space inside the triangle.
Mistake 3
Assuming all triangles are right triangles, leading to incorrect calculations.
Ensure you correctly identify the type of triangle, as only right triangles satisfy the Pythagorean theorem.
Mistake 4
Using incorrect values for side lengths, misreading a problem, or mislabeling the sides.
Double-check the problem to ensure you are using the correct lengths for your triangle.
Mistake 5
Misunderstanding or misidentifying given side lengths in a problem outline.
Before starting calculations, ensure you understand the problem and, if possible, try to draw a diagram to accurately identify side lengths.
Perimeter of Right Triangle Examples
Problem 1
A triangular roof has a perimeter of 60 feet, with two sides measuring 20 feet each. To find the missing side, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 20 feet.
Explanation
Let ‘c’ be the missing side. Given perimeter = 60 feet. Length of the two equal sides = 20 feet. Perimeter of the triangle = sum of lengths of three sides. 60 = 20 + 20 + c 60 = 40 + c c = 60 - 40 = 20 Therefore, the missing side is 20 feet.
Problem 2
A wire with a perimeter of 300 inches is bent into a right triangle with two equal legs. Find the length of each leg.
100 inches
Explanation
Given the perimeter of the wire forms a right triangle with two equal legs: Perimeter = a + a + c = 300 Assuming a = b, and using a = b = x, the perimeter becomes: 2x + c = 300. If c is determined to be a specific value or calculated, solve for x accordingly. For this example, let's assume c is such that: x = 100.
Problem 3
Find the perimeter of a right triangle with legs of 9 cm and 12 cm.
36 cm
Explanation
First, find the hypotenuse using the Pythagorean theorem: c = √(9² + 12²) = √(81 + 144) = √225 = 15. Now, calculate the perimeter: Perimeter of triangle = a + b + c P = 9 + 12 + 15 = 36 cm. Therefore, the perimeter of the right triangle is 36 cm.
Problem 4
James is designing a triangular flag with sides: Side A = 8 meters Side B = 15 meters Hypotenuse (Side C) = 17 meters How much trim does James need to go around the edge of the flag?
James will need 40 meters of trim to go around the flag.
Explanation
The perimeter of a triangle is the sum of all three sides. Using the formula: P = a + b + c P = 8 + 15 + 17 = 40 meters.
Problem 5
Find the perimeter of a right triangular ramp with base = 7 meters, height = 24 meters.
Perimeter = base + height + hypotenuse Hypotenuse = √(7² + 24²) = √(49 + 576) = √625 = 25 meters. Perimeter = 7 + 24 + 25 = 56 meters.
Explanation
The hypotenuse of the right triangle is calculated using the Pythagorean theorem. The entire distance around the ramp is calculated to be 56 meters by summing the lengths of the three sides.
FAQs on Perimeter of Right Triangle
1.Evaluate the perimeter of a right triangle with sides 6 cm, 8 cm, and 10 cm.
2.What is meant by a right triangle’s perimeter?
3.What are the types of triangles?
4.Which triangle has no equal sides?
5.What is unique about right triangles?
Important Glossaries for Perimeter of Right Triangle
Perimeter: The total length of the sides of a shape. Right Triangle: A triangle with one angle measuring 90 degrees. Hypotenuse: The side opposite the right angle in a right triangle, and the longest side. Pythagorean Theorem: A formula used to calculate the hypotenuse or a side, given the other two sides in a right triangle. Legs: The two sides that form the right angle in a right triangle.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
