Triangle Side Analysis: Comparing 8X, 10X, and 9X Side Lengths

Q: What makes a triangle scalene versus other types?

A scalene triangle has all three sides different lengths. An isosceles triangle has exactly two equal sides, and an equilateral triangle has all three sides equal.

Q: Do I need to know the value of X to classify this triangle?

No! Since we're comparing $8X$, $9X$, and $10X$, the variable X cancels out in our comparison. As long as X > 0, these will always be three different lengths.

Q: How do I simplify 7X + 2X?

Combine like terms by adding the coefficients: $7X + 2X = (7 + 2)X = 9X$. Think of it as 7 apples plus 2 apples equals 9 apples!

Q: What if the sides were 8X, 8X, and 10X instead?

Then it would be isosceles because two sides (both $8X$) are equal. Only when all three sides are different do we call it scalene.

Q: Could this triangle actually exist with these side lengths?

Yes! These sides satisfy the triangle inequality: $8X + 9X > 10X$, $8X + 10X > 9X$, and $9X + 10X > 8X$ are all true when X > 0.

Triangle Classification with Algebraic Side Expressions

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

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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

00:06 According to the given side lengths, the triangle is scalene

00:09 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 the triangle below, is it a triangle with different sides?

Step-by-step solution

To determine if the given triangle is scalene, we must examine the sides: $8X$ , $10X$ , and $7X + 2X$ .

Step 1: Simplify the expression for the third side:
$7X + 2X = 9X$ .
Thus, the sides of the triangle are $8X$ , $10X$ , and $9X$ .
Step 2: Compare the side lengths:
- The first side is $8X$ .
- The second side is $10X$ .
- The third side is $9X$ .
Step 3: Check for distinctness of each side:
Since $8X \neq 9X$ , $9X \neq 10X$ , and $8X \neq 10X$ , all sides are indeed different.

Therefore, the triangle is scalene, as all sides have different lengths.

The solution to the problem is: Yes

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Scalene triangles have all three sides with different lengths
Technique: Simplify algebraic expressions first: $7X + 2X = 9X$
Check: Compare all sides: $8X \neq 9X \neq 10X$ confirms scalene ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify algebraic expressions before comparing
Don't compare 8X, 10X, and 7X+2X directly without simplifying = missing that 7X+2X = 9X! This leads to confusion about whether sides are actually different. Always simplify all algebraic expressions first, then compare the results.

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 makes a triangle scalene versus other types?

A scalene triangle has all three sides different lengths. An isosceles triangle has exactly two equal sides, and an equilateral triangle has all three sides equal.

Do I need to know the value of X to classify this triangle?

No! Since we're comparing $8X$ , $9X$ , and $10X$ , the variable X cancels out in our comparison. As long as X > 0, these will always be three different lengths.

How do I simplify 7X + 2X?

Combine like terms by adding the coefficients: $7X + 2X = (7 + 2)X = 9X$ . Think of it as 7 apples plus 2 apples equals 9 apples!

What if the sides were 8X, 8X, and 10X instead?

Then it would be isosceles because two sides (both $8X$ ) are equal. Only when all three sides are different do we call it scalene.

Could this triangle actually exist with these side lengths?

Yes! These sides satisfy the triangle inequality: $8X + 9X > 10X$ , $8X + 10X > 9X$ , and $9X + 10X > 8X$ are all true when X > 0.

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