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

Q: What's the difference between area and perimeter?

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.

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

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

Q: What if the triangle had different side lengths?

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.

Q: How can I remember what perimeter means?

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!

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

Understand the problem

Find the perimeter of the triangle ABC

Step-by-step solution

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

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

Using the formula for the perimeter of a triangle:

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

Substitute the known values:

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

$\text{Perimeter} = 12$

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

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

Final Answer

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 $3^2 + 4^2 = 5^2$ 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

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

FAQ

Everything you need to know about this question

What's the difference between area and perimeter?

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?

It's a special right triangle because $3^2 + 4^2 = 5^2$ (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?

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?

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?

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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