Calculate the Perimeter: Equilateral Triangle with 5-Unit Sides

Q: What makes this triangle equilateral?

An equilateral triangle has all three sides exactly the same length. In this problem, all sides measure 5 units, making it equilateral.

Q: Is there a faster way than adding 5 + 5 + 5?

Yes! Since all sides are equal, use the formula: Perimeter = 3 × side length. So $ 3 \times 5 = 15 $ is much quicker than adding.

Q: What if I forgot the perimeter formula?

No problem! Perimeter always means the distance around the outside of a shape. Just add up all the side lengths: $ 5 + 5 + 5 = 15 $.

Q: Do all triangles use the same perimeter formula?

The basic idea is the same: add all sides. But equilateral triangles have the special shortcut $ 3 \times s $ because all sides are equal.

Equilateral Triangle Perimeter with Given Side Length

The three sides of the triangle ABC are equal. Calculate the perimeter of the triangle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the perimeter of the triangle

00:03 Equal sides according to the given data

00:14 The triangle's perimeter equals the sum of its sides

00:21 Substitute in the side values and proceed to solve for the perimeter

00:26 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The three sides of the triangle ABC are equal. Calculate the perimeter of the triangle.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the side length of the equilateral triangle, which is given as $5$ .
Step 2: Use the formula for the perimeter of an equilateral triangle: $\text{Perimeter} = 3 \times \text{side length}$ .
Step 3: Substitute the given side length into the formula and calculate the perimeter.

Now, let's work through each step:
Step 1: The side length of triangle ABC is $5$ .
Step 2: The perimeter formula for an equilateral triangle is $3 \times s$ , where $s$ is the side length.
Step 3: Plugging in the side length, we get:
$\text{Perimeter} = 3 \times 5 = 15$

Therefore, the perimeter of triangle ABC is $15$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Equilateral triangle has all three sides equal in length
Formula: Perimeter = 3 × side length = 3 × 5 = 15
Check: Count all sides: 5 + 5 + 5 = 15 units ✓

Common Mistakes

Avoid these frequent errors

Adding only two sides or forgetting the third side
Don't calculate 5 + 5 = 10 and stop there! This ignores the third side and gives an incomplete perimeter. Always remember that perimeter means the distance around the entire shape, so you must add all three sides: 5 + 5 + 5 = 15.

Practice Quiz

Test your knowledge with interactive questions

Is the triangle in the drawing a right triangle?

FAQ

Everything you need to know about this question

What makes this triangle equilateral?

An equilateral triangle has all three sides exactly the same length. In this problem, all sides measure 5 units, making it equilateral.

Is there a faster way than adding 5 + 5 + 5?

Yes! Since all sides are equal, use the formula: Perimeter = 3 × side length. So $3 \times 5 = 15$ is much quicker than adding.

What if I forgot the perimeter formula?

No problem! Perimeter always means the distance around the outside of a shape. Just add up all the side lengths: $5 + 5 + 5 = 15$ .

Do all triangles use the same perimeter formula?

The basic idea is the same: add all sides. But equilateral triangles have the special shortcut $3 \times s$ because all sides are equal.

How can I check if my answer is reasonable?

Think logically: if each side is 5 units, the perimeter should be more than 5 but not too much more. An answer like 15 makes sense, but 50 or 150 would be way too big!

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