Calculate Triangle Perimeter: Isosceles Triangle with Sides 6, 6, and 4

Q: What does 'isosceles triangle' mean exactly?

An isosceles triangle has exactly two sides of equal length. In this problem, sides AC and AB both equal 6, while the base BC equals 4.

Q: How do I know which sides are equal from the diagram?

Look for the small marks on the sides! Equal sides have the same markings. You can also check the side length labels - here both AC and AB are labeled as 6.

Q: Does it matter which side is the base?

Not for calculating perimeter! The base is just the side that's different from the two equal sides. Perimeter always equals the sum of all three sides regardless of which is the base.

Q: What if I get the triangle inequality wrong?

The triangle inequality states that any two sides must add up to more than the third side. If this fails, you don't have a valid triangle! Always check: 6+6>4 ✓, 6+4>6 ✓, 6+4>6 ✓.

Triangle Perimeter with Equal Side Lengths

In the triangle ABC, the two legs are equal in length. Calculate the perimeter of the triangle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the perimeter of this triangle.

00:09 The problem tells us that the triangle has equal sides.

00:13 To find the perimeter, we add up all the sides.

00:17 Now, plug in the lengths of the sides and calculate the perimeter.

00:22 Great! That's how you solve for the perimeter.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In the triangle ABC, the two legs are equal in length. Calculate the perimeter of the triangle.

Step-by-step solution

The problem provides us with an isosceles triangle $ABC$ where two sides are equal. According to the diagram and given values, $AC = AB = 6$ and $BC = 4$ .

Step 1: Identify the sides of the triangle.
- Equal sides: $AC = 6$ and $AB = 6$ .
- Base: $BC = 4$ .
Step 2: Calculate the perimeter.
- Use the formula for the perimeter of a triangle: $P = a + b + c$ .
- Substitute the side lengths: $P = 6 + 6 + 4$ .
- Simplify: $P = 16$ .

Therefore, the perimeter of triangle $ABC$ is $16$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Isosceles Rule: Two sides are equal, identify the base side
Addition: Add all three sides: 6 + 6 + 4 = 16
Verification: Check triangle inequality: 6 + 4 > 6 and 6 + 6 > 4 ✓

Common Mistakes

Avoid these frequent errors

Only adding the two equal sides
Don't calculate 6 + 6 = 12 and forget the base! This misses one-third of the triangle's boundary. Always add all three sides: both equal sides plus the base for the complete perimeter.

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 does 'isosceles triangle' mean exactly?

An isosceles triangle has exactly two sides of equal length. In this problem, sides AC and AB both equal 6, while the base BC equals 4.

How do I know which sides are equal from the diagram?

Look for the small marks on the sides! Equal sides have the same markings. You can also check the side length labels - here both AC and AB are labeled as 6.

Does it matter which side is the base?

Not for calculating perimeter! The base is just the side that's different from the two equal sides. Perimeter always equals the sum of all three sides regardless of which is the base.

Can I use a formula for isosceles triangle perimeter?

Yes! For an isosceles triangle with equal sides a and base b, the formula is: $P = 2a + b$ . Here: $P = 2(6) + 4 = 16$ .

What if I get the triangle inequality wrong?

The triangle inequality states that any two sides must add up to more than the third side. If this fails, you don't have a valid triangle! Always check: 6+6>4 ✓, 6+4>6 ✓, 6+4>6 ✓.

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