Triangle Side Analysis: Solving for X when Side Lengths are 2X, X+X, and 6

Q: What's the difference between scalene, isosceles, and equilateral triangles?

Scalene: All three sides are different lengthsIsosceles: Exactly two sides are equalEquilateral: All three sides are equal

Q: Do I need to solve for X to answer this question?

No! You can see directly from the diagram that two sides are both labeled $2X$. Since they're identical expressions, they must be equal regardless of X's value.

Q: What if 2X equals 6? Wouldn't that make all sides equal?

Even if $2X = 6$, the triangle would be equilateral (all sides equal), not scalene. The question asks if it's a triangle with different sides, and the answer is still no.

Q: How can I tell triangle types from algebraic expressions?

Look for identical expressions first! If two sides have the same algebraic expression (like both being $2X$), they're automatically equal. Then compare with remaining sides.

Triangle Classification with Algebraic Side Lengths

Given the values of the sides of a triangle, is it a triangle with different sides?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether the triangle is scalene

00:03 Let's calculate the side

00:07 According to the given side lengths, the triangle is isosceles

00:11 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the values of the sides of a triangle, is it a triangle with different sides?

Step-by-step solution

To determine if this triangle has all different side lengths, we need to check whether the sides $2X$ , $2X$ , and $6$ are all different.

First, note that two sides are given as $2X$ . This immediately indicates these two sides are equal.
Since $2X = 2X$ , these two sides are not different, contradicting the requirement for a scalene (all sides different) triangle.
The third side is $6$ . For a triangle to be scalene, $2X$ would need to be different from $6$ . However, we already have two equal sides $2X$ .

Thus, irrespective of whether the third side $6$ equals $2X$ or not, the presence of two equal sides means the triangle is not scalene.

Therefore, the answer is no, it is not a triangle with different sides.

Therefore, the solution to the problem is: No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Triangle Types: Scalene has all different sides, isosceles has two equal
Identify Equal Sides: Recognize that 2X appears twice in the diagram
Check Classification: Two sides equal means isosceles, not scalene ✓

Common Mistakes

Avoid these frequent errors

Focusing only on whether 2X equals 6
Don't ignore that two sides are both labeled 2X = automatically equal sides! This makes the triangle isosceles regardless of the third side's value. Always check if any two sides are identical first before comparing with the third side.

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's the difference between scalene, isosceles, and equilateral triangles?

Scalene: All three sides are different lengths
Isosceles: Exactly two sides are equal
Equilateral: All three sides are equal

Do I need to solve for X to answer this question?

No! You can see directly from the diagram that two sides are both labeled $2X$ . Since they're identical expressions, they must be equal regardless of X's value.

What if 2X equals 6? Wouldn't that make all sides equal?

Even if $2X = 6$ , the triangle would be equilateral (all sides equal), not scalene. The question asks if it's a triangle with different sides, and the answer is still no.

How can I tell triangle types from algebraic expressions?

Look for identical expressions first! If two sides have the same algebraic expression (like both being $2X$ ), they're automatically equal. Then compare with remaining sides.

Could this triangle be invalid due to triangle inequality?

The question asks about side classification, not validity. However, for any positive value of X, these sides would form a valid triangle since $2X + 2X > 6$ when $X > 1.5$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Triangle questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime