Calculate Isosceles Triangle Perimeter with Side Lengths 9 and 3

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

The problem tells you 'the two legs are equal' and shows sides labeled 9. In an isosceles triangle, the legs are always the two equal sides, while the base is the different side (length 3 here).

Q: What if I mixed up which sides are equal?

If you thought the base was equal to one leg, you'd get perimeter = 3 + 3 + 9 = 15, which is wrong! Always read carefully to identify the two equal legs versus the single different base.

Q: Do I need to check if this forms a valid triangle?

Yes! Use the triangle inequality: each side must be less than the sum of the other two. Here: 9

Q: Can an isosceles triangle have all three sides equal?

No, that would be an equilateral triangle. An isosceles triangle has exactly two equal sides, making it different from both scalene (no equal sides) and equilateral (all equal sides).

Q: What's the difference between legs and base in an isosceles triangle?

The legs are the two equal sides, while the base is the single different side. The base usually sits at the 'bottom' when you draw the triangle, but any side can be the base depending on orientation.

Isosceles Triangle Properties with Given Side Measurements

The two legs of the triangle 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

00:07 The triangle's perimeter equals the sum of its sides

00:13 Substitute in the side values and solve for the perimeter

00:19 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The two legs of the triangle are equal.

Calculate the perimeter of the triangle.

Step-by-step solution

Since the two legs are equal, we know that:

$AB=AC=9$

The perimeter of the triangle is equal to the sum of all sides, therefore:

$AB+AC+BC$

Now let's substitute the known data into the formula and calculate:

$9+9+3=18+3=21$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Isosceles triangle has exactly two equal sides called legs
Technique: Perimeter equals both legs plus base: 9 + 9 + 3
Check: Verify triangle inequality: each side < sum of other two ✓

Common Mistakes

Avoid these frequent errors

Confusing which sides are equal in an isosceles triangle
Don't assume the base is one of the equal sides = wrong perimeter calculation! The problem states 'two legs are equal' meaning the sides of length 9, not the base of length 3. Always identify the two equal legs first, then add the different base.

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

How do I know which sides are the equal legs?

The problem tells you 'the two legs are equal' and shows sides labeled 9. In an isosceles triangle, the legs are always the two equal sides, while the base is the different side (length 3 here).

What if I mixed up which sides are equal?

If you thought the base was equal to one leg, you'd get perimeter = 3 + 3 + 9 = 15, which is wrong! Always read carefully to identify the two equal legs versus the single different base.

Do I need to check if this forms a valid triangle?

Yes! Use the triangle inequality: each side must be less than the sum of the other two. Here: 9 < 9+3 ✓, 9 < 9+3 ✓, and 3 < 9+9 ✓, so it's valid.

Can an isosceles triangle have all three sides equal?

No, that would be an equilateral triangle. An isosceles triangle has exactly two equal sides, making it different from both scalene (no equal sides) and equilateral (all equal sides).

What's the difference between legs and base in an isosceles triangle?

The legs are the two equal sides, while the base is the single different side. The base usually sits at the 'bottom' when you draw the triangle, but any side can be the base depending on orientation.

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