Solve for X: Similar Triangles with Expressions 6X and 10X-58

Similar Triangles with Algebraic Side Expressions

Is it possible to calculate X? If so, what is it?

6X10X-58

❤️ 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 the value of X
00:04 The isosceles triangle, meaning equal sides
00:07 Compare the expressions of the sides
00:11 Arrange the equation so that one side has only the unknown X
00:28 Group like terms
00:35 Isolate X
00:47 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Is it possible to calculate X? If so, what is it?

6X10X-58

2

Step-by-step solution

To solve the problem, we will perform algebraic manipulation to find X X .

The triangle gives expressions for sides: 6X 6X and 10X58 10X - 58 . To find where these are potentially determined equal or prominent in symmetry or division:

  • Set the expressions forming these sides equal to each other:
6X=10X58 6X = 10X - 58

Solve this equation for X X :

  • Subtract 6X 6X from both sides:
0=4X58 0 = 4X - 58
  • Add 58 to both sides:
58=4X 58 = 4X
  • Divide both sides by 4 to solve for X X :
X=584 X = \frac{58}{4}

Upon simplification:

X=14.5 X = 14.5

Therefore, the solution is X=14.5 X = 14.5 , confirmed as the valid solution satisfying provided problem setup.

3

Final Answer

14.5 14.5

Key Points to Remember

Essential concepts to master this topic
  • Similar Triangle Rule: Corresponding sides of similar triangles are proportional to each other
  • Setting Equal: When triangles are similar, set corresponding sides equal: 6X=10X58 6X = 10X - 58
  • Verification: Substitute X = 14.5 back: 6(14.5) = 87 and 10(14.5) - 58 = 87 ✓

Common Mistakes

Avoid these frequent errors
  • Assuming sides must always be equal in similar triangles
    Don't automatically set all corresponding sides equal without understanding the problem setup = wrong equation! Similar triangles have proportional sides, not necessarily equal sides. Always read the diagram carefully to understand what relationship the problem is establishing between the sides.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( 3x=18 \)

FAQ

Everything you need to know about this question

Why are we setting 6X equal to 10X - 58?

+

Looking at the diagram, these expressions represent corresponding sides of similar triangles that appear to be equal in this specific case. The problem is asking us to find when these two sides have the same length.

What if I get a negative value for X?

+

Check your algebra! In this problem, X should be positive since it represents a scaling factor for triangle sides. If you get negative, review your equation setup and solving steps.

How do I know which sides correspond to each other?

+

Look for similar positioning in the triangles and any angle markings. Corresponding sides are opposite to equal angles in similar triangles.

Can I solve this differently?

+

Yes! You could also set up a proportion if you know the triangles are similar: 6X10X58=side 1side 2 \frac{6X}{10X-58} = \frac{\text{side 1}}{\text{side 2}} . But the direct equality method shown here is simpler for this problem.

What does X = 14.5 actually represent?

+

X is a variable that determines the lengths of the triangle sides. When X = 14.5, one side is 6(14.5) = 87 units and the other is 10(14.5) - 58 = 87 units long.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) 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

More Questions

Click on any question to see the complete solution with step-by-step explanations