Perimeter of Triangle: Formula, Examples and Questions

Perimeter of Triangle is the total distance around a triangular figure. It is found by adding the lengths of its three sides. This page explains the perimeter of triangle formula for different triangle types, unit conversion, missing-side calculations, triangle inequality and common perimeter of triangle problems.

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What Is the Perimeter of a Triangle?

The perimeter of a triangle is the sum of the lengths of its three sides. If the sides are a, b and c, then its perimeter is P = a + b + c.

The three side lengths must be expressed in the same unit before addition. For example, a triangle with sides 7 cm, 9 cm and 12 cm has perimeter P = 7 + 9 + 12 = 28 cm. Perimeter is a one-dimensional measurement, so its unit is cm, m or another unit of length, not a square unit.

Perimeter of Triangle Video Lessons

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Triangle Basic Formulas

Learn the basic formulas for triangles, including perimeter, area, and related measurements used in two-dimensional mensuration problems.

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Perimeter of Triangle Formula & Tricks

Important Formulas

General triangle
P = a + b + c

Add the lengths of all three sides of the triangle.

Equilateral triangle
P = 3a

All three sides are equal to a, so the perimeter is three times one side.

Isosceles triangle
P = 2a + b

If two equal sides are a and the third side is b, add twice the equal side and the third side.

Missing side
Missing side = P − sum of the two known sides

Subtract the two known side lengths from the given perimeter.

Unit conversion
1 m = 100 cm; 1 km = 1000 m

Convert every side to the same unit before applying the perimeter formula.

Quick Tricks

Use multiplication for equal sides

For an equilateral triangle, multiply one side by 3. For an isosceles triangle, multiply the equal side by 2 and add the base.

Example: If each side of an equilateral triangle is 11 cm, P = 3 × 11 = 33 cm. If equal sides are 9 cm and the base is 6 cm, P = 2 × 9 + 6 = 24 cm.
Check the triangle inequality

For three lengths a, b and c to form a triangle, the sum of any two sides must be greater than the third side. Equivalently, |a − b| < c < a + b.

Example: Sides 4 cm, 7 cm and 12 cm cannot form a triangle because 4 + 7 = 11, which is less than 12.
Keep units consistent

Convert mixed units before adding the sides. Adding metres directly to centimetres gives an incorrect perimeter.

Example: For sides 2 m, 75 cm and 1 m, convert 2 m and 1 m to centimetres: P = 200 + 75 + 100 = 375 cm, or 3.75 m.

Perimeter of Triangle Concepts

Perimeter of Different Triangle Types

The perimeter formula depends on the equality of the triangle’s sides, but it always represents the sum of all three sides.

For a scalene triangle with sides a, b and c, P = a + b + c. For an isosceles triangle with equal sides a and base b, P = 2a + b. For an equilateral triangle with side a, P = 3a.

Example: A scalene triangle with sides 8 cm, 10 cm and 13 cm has P = 8 + 10 + 13 = 31 cm.

Finding a Missing Side from the Perimeter

A missing side is found by subtracting the two known sides from the total perimeter.

If the perimeter is P and two sides are a and b, the third side is c = P − a − b. The calculated side must also satisfy the triangle inequality with the other two sides.

Example: If P = 24 cm and two sides are 7 cm and 9 cm, the third side is 24 − 7 − 9 = 8 cm.

Perimeter with Different Units

All side lengths must be converted to one unit before they are added.

Use 1 m = 100 cm and 1 km = 1000 m. The final perimeter can be written in the selected unit after the addition.

Example: For sides 1.2 m, 80 cm and 0.5 m, convert to centimetres: 120 + 80 + 50 = 250 cm, which is 2.5 m.

Triangle Inequality and Possible Perimeters

Three positive lengths form a triangle only when the sum of any two lengths is greater than the third length.

For sides a, b and c, the conditions are a + b > c, b + c > a and c + a > b. If the longest side is l and the other sides are x and y, only x + y > l needs to be checked. A third side c with known sides a and b must satisfy |a − b| < c < a + b.

Example: If two sides are 6 cm and 10 cm, the third side must be greater than 4 cm and less than 16 cm.

Perimeter of Triangle Visual Guide

Use the diagram or chart below to understand the concept clearly.

Triangle with three side lengths

Visual guide: Triangle with three side lengths
Side a: a Side b: b Side c: c
The perimeter is obtained by adding the three labelled side lengths.

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Practice Perimeter of Triangle Questions

Practise published questions related to this topic.

1There are 3 classes A, B and C. There are 36, 60 and 72 students in these classes respectively. Each class is to be divided into groups. Each group has same number of students. Each group should have students from only one class. Every student is a part of 1 group. What is the maximum number of students in each group?→ 2An electronics store offers two successive discounts on a laptop priced at ₹51,000. The first discount is 10%, and the second discount is 5%. What is the final price after both discounts are applied?→ 3Gopal observes a 4% increase in sales in the first year and a 20% increase in the second year. If the current sales are ₹249600, what were the sales (in ₹) two years ago?→ 4Simplify √1849 + √529 + 122 - √1521.→ 5The monthly incomes of two friends Manjit and Keshav are in the ratio 5 : 9 respectively and each of them saves ₹48,000 every month. If the ratio of their monthly expenditure is 1 : 3, then find the monthly income of Manjit (in ₹).→ 6Marked price of an article is 20 percent more than its cost price. It is sold at a profit of 10 percent. Marked price of article is Rs. 1200. What is the selling price of the article?→ 7A trader marked the price of an item 40% above the cost price. He allowed two successive discounts of 20% and 25% to a customer. If he incurred a loss of ₹224, at what price did he sell the item to that customer?→ 8The number nearest to 43582 divisible by each of 25, 50 and 75 is -→ 9The sum of the first 5 prime numbers is _____.→ 10A person who spends 75% of his monthly income is able to save ₹4,827 per month. His monthly expenses (in ₹) are:→

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Quick Revision Notes

Perimeter of Triangle Revision Points

Use these formulas and rules to revise perimeter calculations.

  • Perimeter of a triangle is P = a + b + c.
  • For an equilateral triangle, P = 3a.
  • For an isosceles triangle with equal sides a and base b, P = 2a + b.
  • Convert all side lengths to the same unit before addition.
  • To find a missing side, subtract the two known sides from the perimeter.
  • For valid triangle sides, the sum of any two sides must be greater than the third side.
  • Perimeter is measured in linear units such as cm, m or km.

Related Topic Explainers

Area of Square → Perimeter of Square → Area of Rectangle → Perimeter of Rectangle → Area of Triangle →

Perimeter of Triangle FAQs

What is the perimeter of a triangle with sides 5 cm, 8 cm and 11 cm?

P = 5 + 8 + 11 = 24 cm.

What is the perimeter of an equilateral triangle with side 14 m?

For an equilateral triangle, P = 3a = 3 × 14 = 42 m.

How do you find the third side if the perimeter is 30 cm and two sides are 9 cm and 12 cm?

Third side = 30 − 9 − 12 = 9 cm.

Can sides 3 cm, 4 cm and 8 cm form a triangle?

No. The sum of the two smaller sides is 3 + 4 = 7 cm, which is less than 8 cm.

What is the perimeter of a triangle with sides 1 m, 50 cm and 75 cm?

Convert 1 m to 100 cm. The perimeter is 100 + 50 + 75 = 225 cm, or 2.25 m.

What is the difference between the perimeter and area of a triangle?

Perimeter is the sum of the three side lengths and is measured in linear units. Area measures the region inside the triangle and is measured in square units.

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