Calculate Triangle Perimeter: 3-4-5 Right Triangle Challenge

Triangle Perimeter with Special Right Triangle

Find the perimeter of the triangle ABC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's find the perimeter of the triangle. Ready?
00:10 To do this, we'll add up all the sides. The perimeter is the total of all three sides.
00:15 Now, we'll take each side length from our problem. Add them together, and that gives us the perimeter.
00:22 Great job! That's how we find the perimeter of a triangle.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the perimeter of the triangle ABC

333444555AAABBBCCC

2

Step-by-step solution

To find the perimeter of triangle ABC \triangle ABC , we need to sum the lengths of its sides:

  • Side AB=3 AB = 3
  • Side BC=4 BC = 4
  • Side CA=5 CA = 5

Using the formula for the perimeter of a triangle:

Perimeter=AB+BC+CA \text{Perimeter} = AB + BC + CA

Substitute the known values:

Perimeter=3+4+5 \text{Perimeter} = 3 + 4 + 5

Perimeter=12 \text{Perimeter} = 12

Thus, the perimeter of triangle ABC \triangle ABC is 12\mathbf{12}.

From the multiple-choice options provided, the correct choice is option 1: 12.

3

Final Answer

12

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perimeter equals the sum of all three side lengths
  • Technique: Add each side: 3 + 4 + 5 = 12
  • Check: Verify all sides are included in addition: AB + BC + CA ✓

Common Mistakes

Avoid these frequent errors
  • Using the Pythagorean theorem instead of adding sides
    Don't calculate 32+42=52 3^2 + 4^2 = 5^2 to find perimeter! This formula finds if a triangle is a right triangle, not its perimeter. Always add all three side lengths directly for perimeter.

Practice Quiz

Test your knowledge with interactive questions

Find the perimeter of the triangle ABC

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FAQ

Everything you need to know about this question

What's the difference between area and perimeter?

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Perimeter is the distance around the triangle (adding all sides), while area is the space inside the triangle. For perimeter, just add: 3 + 4 + 5 = 12.

Why is this called a 3-4-5 triangle?

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It's a special right triangle because 32+42=52 3^2 + 4^2 = 5^2 (9 + 16 = 25). The sides follow the Pythagorean theorem perfectly, making it a common example in geometry.

Do I need to use any formulas for this problem?

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No complex formulas needed! The perimeter formula is simply: P = side₁ + side₂ + side₃. Just add the three given lengths together.

What if the triangle had different side lengths?

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The method stays the same - always add all three sides. Whether it's 2-7-9 or 10-15-20, perimeter is just the sum of all side lengths.

How can I remember what perimeter means?

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Think of "perimeter" as walking around the edge of the triangle. You'd walk along each side once, so you add up all the side lengths!

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