Find X in an Equilateral Triangle with 33cm Perimeter

Perimeter Problems with Equilateral Triangles

Below is an equilateral triangle:

XXX

If the perimeter of the triangle is 33 cm, then what is the value of X?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the value of X
00:03 The triangle is equilateral therefore all sides equal X
00:07 The perimeter is equal to the sum of the triangle's sides
00:10 Substitute in the relevant values and solve
00:14 Isolate X
00:22 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Below is an equilateral triangle:

XXX

If the perimeter of the triangle is 33 cm, then what is the value of X?

2

Step-by-step solution

We know that in an equilateral triangle all sides are equal.

Therefore, if we know that one side is equal to X, then all sides are equal to X.

We know that the perimeter of the triangle is 33.

The perimeter of the triangle is equal to the sum of the sides together.

We replace the data:

x+x+x=33 x+x+x=33

3x=33 3x=33

We divide the two sections by 3:

3x3=333 \frac{3x}{3}=\frac{33}{3}

x=11 x=11

3

Final Answer

11

Key Points to Remember

Essential concepts to master this topic
  • Property: All three sides of an equilateral triangle are equal
  • Formula: Perimeter = 3x, so 3x = 33 means x = 11
  • Check: Verify that 11 + 11 + 11 = 33 cm perimeter ✓

Common Mistakes

Avoid these frequent errors
  • Thinking X represents the perimeter instead of one side length
    Don't assume X = 33 because that's the perimeter = wrong answer! X represents one side, not the total distance around. Always remember that perimeter equals the sum of all sides, so 3X = 33.

Practice Quiz

Test your knowledge with interactive questions

In a right triangle, the side opposite the right angle is called....?

FAQ

Everything you need to know about this question

Why are all sides equal in an equilateral triangle?

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That's the definition of equilateral! The prefix 'equi-' means equal, and 'lateral' means sides. So an equilateral triangle has three equal sides by definition.

How is this different from other triangles?

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Equilateral: all 3 sides equal
Isosceles: only 2 sides equal
Scalene: all 3 sides different lengths

What if the triangle wasn't equilateral?

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Then you'd need to know the individual lengths of each side to find the perimeter. With equilateral triangles, knowing one side tells you everything!

Can I use this method for other shapes?

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Yes! For any regular polygon (equal sides), use: Perimeter = (number of sides) × (side length). For example, a square: P = 4s.

What if my answer doesn't divide evenly?

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Sometimes you'll get a decimal or fraction for the side length. That's perfectly normal! Just make sure your calculation is accurate.

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