1. What is the Scale Factor?

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

2. How Does the Calculator Work?

The calculator uses the scale factor equation:

Where:

• \( k \) — Scale factor (unitless)
• \( side_{new} \) — Length of side in new figure
• \( side_{old} \) — Length of corresponding side in original figure

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

3. Importance of Scale Factor

Details: Scale factor is crucial in geometry for determining proportional relationships between similar figures, calculating area/volume ratios (k² and k³ respectively), and in real-world applications like map scaling and model building.

4. Using the Calculator

Tips: Enter both side lengths in the same units. The calculator will determine the scale factor between them. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How does scale factor relate to area and volume?
A: Area scales by k², volume by k³. A figure twice as large (k=2) has 4 times the area and 8 times the volume.

Q2: Can scale factor be negative?
A: In pure scaling, no. Negative values typically indicate reflection combined with scaling.

Q3: What's the difference between scale factor and ratio?
A: Scale factor is a specific type of ratio comparing corresponding dimensions of similar figures.

Q4: How is scale factor used in real life?
A: Common in architecture (blueprints), cartography (maps), model building, and image resizing.

Q5: What if my figures aren't similar?
A: The scale factor concept only applies to similar figures where all corresponding angles are equal and sides are proportional.