Solve for X: Finding the Side Length in an Isosceles Triangle with Perimeter 50

Isosceles Triangle Perimeter with Equal Sides

Look at the isosceles triangle below:

5.65.65.6XXX

The perimeter of the triangle is 50.

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 In an isosceles triangle there is a pair of equal sides
00:03 The perimeter formula of a triangle is the sum of its sides
00:09 Insert the known data into the formula
00:16 Move terms to the other side
00:24 Divide by 2 to isolate the unknown
00:31 That's the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the isosceles triangle below:

5.65.65.6XXX

The perimeter of the triangle is 50.

What is the value of X?

2

Step-by-step solution

Since we know the triangle is isosceles, the other side will also be equal to X

Now we can replace the data to calculate X.

The perimeter of the triangle is equal to:

x+x+5.6=50 x+x+5.6=50

2x=505.6 2x=50-5.6

2x=44.4 2x=44.4

We divide both sides by 2:

2x2=44.42 \frac{2x}{2}=\frac{44.4}{2}

x=22.2 x=22.2

3

Final Answer

22.2

Key Points to Remember

Essential concepts to master this topic
  • Isosceles Rule: Two sides are equal in an isosceles triangle
  • Technique: Set up equation as x + x + 5.6 = 50
  • Check: Verify 22.2 + 22.2 + 5.6 = 50 ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all three sides are equal
    Don't set up the equation as 3x = 50 = x = 16.67! This treats the triangle as equilateral instead of isosceles, giving a completely wrong answer. Always identify which two sides are equal in an isosceles triangle.

Practice Quiz

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In a right triangle, the side opposite the right angle is called....?

FAQ

Everything you need to know about this question

How do I know which sides are equal in an isosceles triangle?

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Look for matching labels or markings! In this problem, both sides coming from the top vertex are labeled 'X', while the base is labeled '5.6'. The two sides with the same label are equal.

What if I can't tell which triangle type it is?

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The problem tells you it's isosceles! This means exactly two sides are equal. If all three were equal, it would be called equilateral instead.

Why do I add x + x instead of just using x?

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Because there are two sides of length x! Perimeter means adding up all three sides: the two equal sides (x + x) plus the base (5.6).

Can I solve this a different way?

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Yes! You could write it as 2x+5.6=50 2x + 5.6 = 50 from the start. This is the same as x + x + 5.6 = 50, just written more compactly.

What if my answer doesn't make sense geometrically?

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Always check if your answer creates a valid triangle! The sum of any two sides must be greater than the third side. Here: 22.2 + 22.2 > 5.6 ✓

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