Triangle Side Lengths: Solve for X When 2X + 3X + 3.5X = 17

Linear Equations with Variable Coefficients

Look at the following triangle:

2X2X2X3.5X3.5X3.5X3X3X3X

The perimeter of the triangle is 17.

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 X
00:03 The perimeter is equal to the sum of the triangle's sides
00:09 Substitute the appropriate values into the formula and solve
00:16 Isolate X
00:25 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following triangle:

2X2X2X3.5X3.5X3.5X3X3X3X

The perimeter of the triangle is 17.

What is the value of X?

2

Step-by-step solution

We know that the perimeter of a triangle is equal to the sum of all sides together, so we replace the data:

3x+2x+3.5x=17 3x+2x+3.5x=17

8.5x=17 8.5x=17

Divide the two sections by 8.5:

8.5x8.5=178.5 \frac{8.5x}{8.5}=\frac{17}{8.5}

x=2 x=2

3

Final Answer

2

Key Points to Remember

Essential concepts to master this topic
  • Perimeter Rule: Sum all sides of a triangle to find perimeter
  • Combining: Add like terms: 2x+3x+3.5x=8.5x 2x + 3x + 3.5x = 8.5x
  • Check: Substitute x = 2: 2(2) + 3(2) + 3.5(2) = 4 + 6 + 7 = 17 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to combine like terms before solving
    Don't try to solve 2x+3x+3.5x=17 2x + 3x + 3.5x = 17 without combining terms first = three separate unknowns instead of one! This makes the problem unsolvable. Always combine like terms to get 8.5x=17 8.5x = 17 first.

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 do I add the coefficients 2 + 3 + 3.5?

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When you have like terms (all containing x), you add their coefficients! Think of it as 2x+3x+3.5x 2x + 3x + 3.5x = (2 + 3 + 3.5) × x = 8.5x 8.5x .

What if I get a decimal coefficient like 8.5?

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That's totally normal! Just divide both sides: 178.5=2 \frac{17}{8.5} = 2 . You can also convert to fractions if you prefer: 8.5=172 8.5 = \frac{17}{2} .

How do I know this triangle actually exists?

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Check the triangle inequality! The sum of any two sides must be greater than the third side. With x = 2: sides are 4, 6, and 7, and 4 + 6 > 7 ✓

Can I solve this without combining like terms?

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Technically you could, but it's much harder! Combining like terms first turns a complex equation into a simple one-step division problem.

What does perimeter mean again?

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Perimeter is the distance around the outside of a shape. For triangles, just add up all three side lengths to get the total distance around!

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