1. What is the Scale Factor?

The scale factor (k) is the ratio of corresponding lengths in two similar geometric figures. For triangles, it describes how much larger or smaller one triangle is compared to another.

2. How Does the Calculator Work?

The calculator uses the scale factor formula:

Where:

• \( k \) — Scale factor (dimensionless)
• \( Side1 \) — Length of side in original triangle
• \( Side2 \) — Length of corresponding side in scaled triangle

Explanation: The scale factor is constant for all corresponding sides in similar figures. A scale factor >1 means enlargement, <1 means reduction.

3. Importance of Scale Factor

Details: Scale factors are crucial in geometry for solving problems involving similar figures, map scaling, model building, and understanding proportional relationships.

4. Using the Calculator

Tips: Enter lengths of corresponding sides from two similar triangles. Both values must be positive numbers. The units must match (calculator doesn't convert units).

5. Frequently Asked Questions (FAQ)

Q1: Can the scale factor be negative?
A: No, scale factors are always positive as lengths are always positive.

Q2: How is scale factor related to area and volume?
A: Area scales by \( k^2 \), volume by \( k^3 \). A triangle with scale factor 2 will have 4 times the area.

Q3: What if the triangles aren't similar?
A: The calculator assumes similarity. If triangles aren't similar, corresponding side ratios won't be equal.

Q4: How precise should my measurements be?
A: Use the same precision for both measurements. More precise inputs yield more accurate scale factors.

Q5: Can I use this for other shapes?
A: Yes, the same principle applies to any similar polygons or 3D shapes.