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Isosceles Triangle Length Calculator

Isosceles Triangle Formulas:

\[ \text{Base} = 2 \times \sqrt{\text{leg}^2 - \left(\frac{\text{Perimeter}}{2} - \text{leg}\right)^2} \] \[ \text{Leg} = \frac{\text{Perimeter}}{2} - \frac{\text{Base}}{2} \] \[ \text{Height} = \sqrt{\text{leg}^2 - \left(\frac{\text{Base}}{2}\right)^2} \]

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1. What is an Isosceles Triangle?

An isosceles triangle is a triangle with at least two sides of equal length. The angles opposite the equal sides are also equal. This calculator helps you find missing dimensions of an isosceles triangle when you know certain other measurements.

2. How Does the Calculator Work?

The calculator uses geometric formulas specific to isosceles triangles to calculate:

3. Important Formulas

\[ \text{Base} = 2 \times \sqrt{\text{leg}^2 - \left(\frac{\text{Perimeter}}{2} - \text{leg}\right)^2} \] \[ \text{Leg} = \frac{\text{Perimeter}}{2} - \frac{\text{Base}}{2} \] \[ \text{Height} = \sqrt{\text{leg}^2 - \left(\frac{\text{Base}}{2}\right)^2} \]

Where:

4. Using the Calculator

Steps:

  1. Select what you want to calculate (base, leg, or height)
  2. Enter the known values
  3. Click "Calculate" to get the result
Note: All values must be positive numbers that satisfy triangle inequality conditions.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between isosceles and equilateral?
A: Equilateral triangles have all three sides equal, while isosceles have only two equal sides.

Q2: Can I calculate area with this calculator?
A: Not directly, but you can calculate height first, then use Area = (base × height)/2.

Q3: What if my perimeter is less than twice the leg length?
A: This violates triangle inequality - such a triangle cannot exist.

Q4: How accurate are the calculations?
A: Results are accurate to two decimal places when valid inputs are provided.

Q5: Can I use this for right isosceles triangles?
A: Yes, but specialized formulas exist for right triangles that might be simpler.

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