Solve for X: Triangle with Sides 2X, 3X, and 3.5X Having 17cm Perimeter

Q: Why do all the sides have X in them?

The sides are proportional to each other! This means they're all related by the same scaling factor X. When X = 2, the sides become 4 cm, 6 cm, and 7 cm.

Q: How do I combine 2X + 3X + 3.5X?

Think of X as a common factor: 2X + 3X + 3.5X = (2 + 3 + 3.5)X = 8.5X. It's like combining 2 apples + 3 apples + 3.5 apples = 8.5 apples!

Q: Can triangles have sides with decimals like 3.5X?

Absolutely! Side lengths can be any positive number, including decimals. When X = 2, the side 3.5X becomes 7 cm, which is a perfectly valid triangle side.

Q: How do I know if my triangle is valid?

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

Perimeter Equations with Variable Coefficients

The perimeter of the triangle ABC is equal to 17 cm.

Calculate X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the value of X

00:03 The perimeter of the triangle equals the sum of its sides

00:07 Substitute in the relevant values according to the given data and proceed to solve for X

00:16 Collect like terms

00:20 Substitute in the perimeter value and isolate the unknown X

00:26 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The perimeter of the triangle ABC is equal to 17 cm.

Calculate X.

Step-by-step solution

The solution involves calculating the unknown $X$ using the perimeter provided for the triangle ABC:

The equation representing the perimeter of triangle ABC is:
$2X + 3X + 3.5X = 17$ .
Combine like terms:
$8.5X = 17$ .
To find $X$ , divide both sides by 8.5:
$X = \frac{17}{8.5}$ .
Calculate the division:
$X = 2$ .
Verify by checking the perimeter with $X = 2$ :
$2 \times 2 + 3 \times 2 + 3.5 \times 2 = 4 + 6 + 7 = 17$ , which matches the given perimeter.

Thus, the value of $X$ is $2$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: Add all sides to get total perimeter
Combining Terms: $2X + 3X + 3.5X = 8.5X$
Verification: Check by substituting: $2(2) + 3(2) + 3.5(2) = 4 + 6 + 7 = 17$ ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients incorrectly when combining like terms
Don't add 2 + 3 + 3.5 = 8.5 then multiply by X = wrong setup! This treats X as a separate multiplier instead of part of each term. Always combine like terms: 2X + 3X + 3.5X = 8.5X, then solve 8.5X = 17.

Practice Quiz

Test your knowledge with interactive questions

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

FAQ

Everything you need to know about this question

Why do all the sides have X in them?

The sides are proportional to each other! This means they're all related by the same scaling factor X. When X = 2, the sides become 4 cm, 6 cm, and 7 cm.

How do I combine 2X + 3X + 3.5X?

Think of X as a common factor: 2X + 3X + 3.5X = (2 + 3 + 3.5)X = 8.5X. It's like combining 2 apples + 3 apples + 3.5 apples = 8.5 apples!

What if I get a decimal answer for X?

Decimal answers are completely normal! In this problem, X = 2 is a whole number, but many similar problems have decimal solutions. Always check your work by substituting back.

Can triangles have sides with decimals like 3.5X?

Absolutely! Side lengths can be any positive number, including decimals. When X = 2, the side 3.5X becomes 7 cm, which is a perfectly valid triangle side.

How do I know if my triangle is valid?

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

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Solve for X: Triangle with Sides 2X, 3X, and 3.5X Having 17cm Perimeter

Perimeter Equations with Variable Coefficients

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do all the sides have X in them?

How do I combine 2X + 3X + 3.5X?

What if I get a decimal answer for X?

Can triangles have sides with decimals like 3.5X?

How do I know if my triangle is valid?

🌟 Unlock Your Math Potential

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