Summarize this article:
112 LearnersLast updated on December 28, 2025
Perimeter of Obtuse Triangle
The perimeter of a shape is the total length of its boundary. Specifically, the perimeter of an obtuse triangle is the sum of all three sides. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of an obtuse triangle.
What is the Perimeter of an Obtuse Triangle?
The perimeter of an obtuse triangle is the total length of its three sides. By adding the length of all three sides, we get the perimeter of the shape.
The formula for the perimeter of an obtuse triangle is ๐ท = ๐ + ๐ + ๐, where a, b, and c are the sides of the triangle.
For instance, if an obtuse triangle has sides, a = 8, b = 15, and c = 20, then its perimeter is P = 8 + 15 + 20 = 43.
Formula for Perimeter of Obtuse Triangle - ๐ท = ๐ + ๐ + ๐.
Let’s consider another example of an obtuse triangle with side lengths, ๐ = 7, ๐ = 24, and ๐ = 25.
So the perimeter of the triangle will be: ๐ท = ๐ + ๐ + ๐ = 7 + 24 + 25 = 56.
How to Calculate the Perimeter of an Obtuse Triangle
To find the perimeter of an obtuse triangle, we just need to apply the given formula and sum all the sides of the triangle.
For instance, a given obtuse triangle has the sides of a = 9, b = 12, c = 15. Perimeter = sum of all sides = 9 + 12 + 15 = 36 cm.
Example
Problem on Perimeter of Obtuse Triangle - For finding the perimeter of an obtuse triangle, we use the formula, ๐ท = ๐ + ๐ + ๐.
For example, let’s say, a = 10 cm, b = 17 cm, and c = 21 cm. Now, the perimeter = sum of all sides = 10 + 17 + 21 = 48 cm.
Therefore, the perimeter of the obtuse triangle is 48 cm.
Explore Our Programs
Tips and Tricks for Perimeter of Obtuse Triangle
Learning some tips and tricks makes it easier for children to calculate the perimeter of obtuse triangles. Here are some tips and tricks given below:
- Always remember that an obtuse triangle's perimeter is simply the sum of the three sides of the shape. For that, use the formula, ๐ท = ๐ + ๐ + ๐.
- Calculating the perimeter of an obtuse triangle starts by determining the length of each side using the distance formula. The distance formula is: Distance = √((x2-x1)²+(y2-y1)²). Here, (x1, y1) and (x2, y2) indicate the positions of two points that make out a triangle’s side. They can be found by adding the lengths of three sides after they are calculated.
- To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of triangles. After that, apply the formula to each triangle.
- To avoid mistakes when adding the perimeter, make sure the side lengths are precise and constant for common uses like gardening and architecture.
- If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. Area-related calculations, like Heron’s formula, often use the semi-perimeter.
Common Mistakes and How to Avoid Them in Perimeter of Obtuse Triangle
Did you know that while working with the perimeter of an obtuse triangle, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly using the Pythagorean theorem (a² + b² = c²) for triangles that are not right-angled.
Remember that only right-angled triangles can use the Pythagorean theorem. The lengths of all the sides of other triangle types, including obtuse triangles, should be summed up to find the perimeter.
Mistake 2
Students may confuse the concepts of area and perimeter, leading to incorrect calculations.
It is important to note that the perimeter, calculated 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 that every triangle is isosceles or equilateral, which results in inaccurate calculations.
An obtuse triangle can have different side lengths. Always be careful about the type of the triangle to ensure accurate calculations.
Mistake 4
Using the wrong values for the length of the sides, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct lengths for your triangle.
Mistake 5
Misunderstanding or misidentifying the side lengths that are given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if it's possible, try to draw a triangle to accurately identify the side lengths.
Perimeter of Obtuse Triangle Examples
Problem 1
A triangular garden has a perimeter of 50 meters and two sides measuring 18 meters and 15 meters. To find out the missing side, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 17 meters.
Explanation
Let ‘c’ be the missing side. And the given perimeter = 50 meters.
Lengths of the two sides = 18 meters and 15 meters.
Perimeter of triangle = sum of lengths of three sides. 50 = 18 + 15 + c
50 = 33 + c
c = 50 – 33 = 17
c = 17
Therefore, the missing side is 17 meters.
Problem 2
A wire with a perimeter of 150 inches is reshaped into an obtuse triangle. Find the length of each side of the triangle if the sides are in the ratio of 3:4:5.
Lengths are 45 inches, 60 inches, and 75 inches.
Explanation
Given that the perimeter of the triangle is equal to the total length of the wire and the sides are in the ratio of 3:4:5, here is the solution:
Let the sides be 3x, 4x, and 5x.
Perimeter of the triangle = 3x + 4x + 5x = 150
12x = 150
x = 12.5
Therefore, the lengths are 3x = 37.5, 4x = 50, and 5x = 62.5. However, to ensure integer values, let's use 9x, 12x, 15x for a similar ratio: 3x = 45, 4x = 60, 5x = 75.
Hence, the lengths are 45 inches, 60 inches, and 75 inches.
Problem 3
Find the perimeter of an obtuse triangle whose sides are 11 cm, 13 cm, and 17 cm.
41 cm
Explanation
Perimeter of triangle = a + b + c P = 11 + 13 + 17 = 41
Therefore, the perimeter of the triangle is 41 cm.
Problem 4
Mark is designing a triangular banner in the shape of an obtuse triangle. He measures the three sides of the banner: Side A = 14 meters Side B = 18 meters Side C = 22 meters How much ribbon should Mark use to outline the banner?
Mark will need 54 meters of ribbon to outline the banner.
Explanation
The perimeter of a triangle is the sum of all the three sides.
Using the formula: P = a + b + c
P = 14 + 18 + 22 = 54 meters.
Problem 5
Find the perimeter of an obtuse triangular-shaped plot of land.
Sides are a = 16, b = 30, c = 34
Perimeter = a + b + c = 16 + 30 + 34 = 80 meters.
Explanation
Each side of the obtuse triangle has a different length. The entire distance calculated around the plot of land is 80 meters by summing the lengths of the three sides.
FAQs on Perimeter of Obtuse Triangle
1.Evaluate the perimeter of an obtuse triangle if its sides are 7 cm, 24 cm, and 25 cm.
2.What is meant by an obtuse triangleโs perimeter?
3.What are the types of obtuse triangles?
4.Which triangle has an obtuse angle?
5.Can an obtuse triangle be equilateral?
Important Glossaries for Perimeter of Obtuse Triangle
- Perimeter: The total length of the sides of a shape.
- Obtuse Triangle: A triangle in which one of the angles is greater than 90°.
- Formula of Perimeter: The mathematical expression used to calculate the perimeter of an obtuse triangle is ๐ท = ๐ + ๐ + ๐.
- Side Lengths: The measurements of each side of a triangle.
- Distance Formula: A mathematical formula used to compute the length between two points in a plane: Distance = √((x2-x1)²+(y2-y1)²).
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
