Triangle Side Lengths: Is 2X, 2X, 4X an Equilateral Triangle?

Triangle Classification with Variable Expressions

Given the size of the 3 sides of the triangle, is it an equilateral triangle?

2X2X2XAAACCCBBB4X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's find out if this triangle is equilateral.
00:13 Given the side lengths, this triangle is scalene.
00:17 And there you have it! That's our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the size of the 3 sides of the triangle, is it an equilateral triangle?

2X2X2XAAACCCBBB4X

2

Step-by-step solution

To determine if the triangle is equilateral, let's check the lengths of its sides:

  • The first side is 2X 2X .
  • The second side is 2X 2X .
  • The third side is 4X 4X .

For a triangle to be equilateral, all side lengths must be the same, i.e., 2X=2X=4X 2X = 2X = 4X . Clearly, 2X4X 2X \neq 4X . Therefore, the sides are not equal.

Given that not all sides are of equal length, the triangle is not equilateral.

Therefore, the correct answer is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Equilateral Rule: All three sides must have identical lengths
  • Compare Method: Check if 2X=2X=4X 2X = 2X = 4X by inspection
  • Verify Logic: Since 2X4X 2X \neq 4X for any positive X, not equilateral ✓

Common Mistakes

Avoid these frequent errors
  • Assuming equal variables mean equal triangle
    Don't think having the same variable X makes all sides equal = wrong classification! The coefficients (2, 2, 4) are different, so 2X ≠ 4X. Always compare the complete expressions, not just the variables.

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

What if X has a specific value like X = 3?

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Even with a specific value, the sides would be 6, 6, and 12. Since 6 ≠ 12, it's still not equilateral. The variable value doesn't change the relationship between coefficients.

Could this triangle be isosceles instead?

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Yes! Since two sides are 2X 2X (equal length), this is an isosceles triangle with two equal sides and one different side.

What does X represent in this problem?

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X is a positive variable representing a unit of measurement. It could be inches, centimeters, or any length unit. The key is comparing the coefficients (2, 2, 4).

How do I remember what makes a triangle equilateral?

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Think "equi" = equal and "lateral" = sides. All three sides must be exactly the same length. If even one side is different, it's not equilateral!

Can X be zero or negative?

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For a valid triangle, X must be positive. Zero would make all sides zero (no triangle), and negative values don't make sense for lengths in geometry.

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