Perimeter of Two Triangles
2026-02-21 21:11 Diff
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Last updated on December 28, 2025

The perimeter of a shape is the total length of its boundary. The sum of all three sides is called the perimeter of a triangle. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of two triangles.

What is the Perimeter of Two Triangles?

The perimeter of two triangles is the combined total length of their six sides. By adding the length of all sides from both triangles, we get the total perimeter.

The formula for the perimeter of a single triangle is  P = a + b + c , where  a ,  b , and  c  are the sides of the triangle.

For instance, if two triangles have sides\(  a_1 = 5, b_1 = 7, c_1 = 9\)  and  \(a_2 = 4, b_2 = 6, c_2 = 8 \), then their combined perimeter is\( ( P = (5 + 7 + 9) + (4 + 6 + 8) = 39 ).\)

Formula for Perimeter of Two Triangles - ( P = (a_1 + b_1 + c_1) + (a_2 + b_2 + c_2) ).

Let’s consider another example of two triangles with side lengths\( ( a_1 = 6, b_1 = 8, c_1 = 10 ) \) and \(( a_2 = 7, b_2 = 9, c_2 = 5 )\).

So the combined perimeter of the two triangles will be: \( P = (6 + 8 + 10) + (7 + 9 + 5) = 45 \).

How to Calculate the Perimeter of Two Triangles

To find the perimeter of two triangles, we just need to apply the given formula and sum all the sides of both triangles.

For instance, given triangles have sides\( ( a_1 = 3, b_1 = 4, c_1 = 5 ) and ( a_2 = 6, b_2 = 7, c_2 = 8 ).\)

Perimeter = sum of all sides = ( (3 + 4 + 5) + (6 + 7 + 8) = 33 ).

Example

Problem on Perimeter of Two Triangles -

For finding the perimeter of two triangles, we use the formula, \(( P = (a_1 + b_1 + c_1) + (a_2 + b_2 + c_2) )\).

For example, let’s say,\( ( a_1 = 2 \, \text{cm}, b_1 = 3 \, \text{cm}, c_1 = 4 \, \text{cm} ) and ( a_2 = 5 \, \text{cm}, b_2 = 6 \, \text{cm}, c_2 = 7 \, \text{cm} ). \)

Now, the perimeter = sum of all sides =  (2 + 3 + 4) + (5 + 6 + 7) = 27 cm .

Therefore, the combined perimeter of the two triangles is 27 cm.

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Tips and Tricks for Perimeter of Two Triangles

Learning some tips and tricks makes it easier for children to calculate the perimeter of two triangles. Here are some tips and tricks given below:

  • Always remember that a triangle's perimeter is simply the sum of the three sides of the shape. For two triangles, use the formula, \(( P = (a_1 + b_1 + c_1) + (a_2 + b_2 + c_2) ).\)
  • Calculating the perimeter of triangles starts by determining the length of each side using the distance formula. The distance formula is: Distance = \(( \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} ).\) Here, \\((x_1, y_1) and (x_2, y_2)\)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 Two Triangles

Did you know that while working with the perimeter of two triangles, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:

Problem 1

Two triangular flower beds have perimeters of 50 inches and 60 inches, respectively. If one of the flower beds is missing a side measuring 18 inches, find the perimeter of both flower beds combined.

Okay, lets begin

The combined perimeter is 110 inches.

Explanation

Let ‘b’ be the side of the missing side of the first flower bed. And the given perimeter of the first flower bed = 50 inches. One side is missing, and the other two sides are known: 16 inches and 18 inches.

Perimeter of the first triangle = sum of lengths of three sides.  50 = 16 + 18 + b 

50 = 34 + b 

 b = 50 - 34 = 16

Therefore, the missing side is 16 inches. Combined perimeter = 50 + 60 = 110 inches.

Well explained 👍

Problem 2

A piece of wire 312 inches long is cut into two parts and shaped into two equilateral triangles. Find the length of each side of both triangles if they are equal in size.

Okay, lets begin

52 inches

Explanation

Given that the total length of the wire is 312 inches, it is shaped into two equilateral triangles of equal size.

Perimeter of each triangle = Total length of the wire divided by 2

Perimeter of each equilateral triangle = \(3 × a ( 156 = 3 × a ) ( 156 ÷ 3 = 52 ) ( a = 52 )\) Therefore, the length of each side of both triangles is 52 inches.

Well explained 👍

Problem 3

Find the combined perimeter of two equilateral triangles whose sides are 9 cm and 11 cm, respectively.

Okay, lets begin

60 cm

Explanation

Perimeter of the first triangle = \( 3 \times 9 = 27 cm\)

Perimeter of the second triangle =\( 3 \times 11 = 33 cm \)

Combined perimeter = 27 + 33 = 60 cm

Therefore, the combined perimeter of the two triangles is 60 cm.

Well explained 👍

Problem 4

Liam is planning two triangular areas for a playground, measuring the sides of the first triangle as 10 meters, 12 meters, and 14 meters, and the second as 8 meters, 15 meters, and 9 meters. How much fencing should Liam buy to go around both areas?

Okay, lets begin

Liam will need 68 meters of fencing to go around both areas.

Explanation

The perimeter of the first triangle is the sum of all three sides: \( P_1 = 10 + 12 + 14 = 36 \)meters.

The perimeter of the second triangle is the sum of all three sides: \( P_2 = 8 + 15 + 9 = 32 \) meters.

Combined perimeter = \\(P_1 + P_2 = 36 + 32 = 68 \) meters.

Well explained 👍

Problem 5

Calculate the combined perimeter of two scalene triangular rocks.

Okay, lets begin

Sides of the first triangle are  a = 5, b = 12, c = 13

Sides of the second triangle area = 7, b = 9, c = 14

Combined perimeter = (5 + 12 + 13) + (7 + 9 + 14) = 60 meters.

Explanation

Each side of the scalene triangles has different lengths. The entire distance around both rocks is calculated to be 60 meters by summing the lengths of the sides of both triangles.

Well explained 👍

FAQs on Perimeter of Two Triangles

1.Evaluate the combined perimeter of two triangles if their sides are 4 cm, 5 cm, and 7 cm for the first, and 6 cm, 8 cm, and 11 cm for the second.

Combined perimeter of the two triangles =  (4 + 5 + 7) + (6 + 8 + 11) = 41 cm.

2.What is meant by the perimeter of two triangles?

The perimeter is the total length around the sides of two triangles. In other words, it is the sum of the lengths of all six sides.

3.What are the types of triangles?

There are six types of triangles: Equilateral triangle, Isosceles triangle, Scalene triangle, Acute triangle, Right triangle, and Obtuse triangle.

4.Which triangle has no equal sides?

A scalene triangle is a triangle with no equal sides. All three sides of the scalene triangle are different.

5.Which triangle has the smallest perimeter?

The orthic triangle has the smallest perimeter.

Important Glossaries for Perimeter of Two Triangles

  • Perimeter: The total length of the sides of a shape.
  • Triangle: A polygon with three sides and three angles.
  • Scalene Triangle: A triangle with all three sides of different lengths.
  • Equilateral Triangle: A triangle with all three sides of equal length.
  • Formula of Perimeter: The mathematical expression used to calculate the perimeter of two triangles is \( P = (a_1 + b_1 + c_1) + (a_2 + b_2 + c_2) .\)

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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.

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: She has songs for each table which helps her to remember the tables