Triangle Scale Factor Calculator

Find the scale factor between two similar triangles, along with perimeter ratio and area ratio.

Enter Corresponding Sides

Triangle 1 (Original)
Triangle 2 (Scaled)

Result

Scale Factor (k)
--
Ratio a'/a --
Ratio b'/b --
Ratio c'/c --
Consistent Ratios? --
Perimeter Ratio (k) --
Area Ratio (k²) --
Perimeter 1 --
Perimeter 2 --

Step-by-Step Solution

k = a'/a = b'/b = c'/c

Understanding Scale Factor in Similar Triangles

When two triangles are similar, all corresponding sides are in the same ratio. This common ratio is called the scale factor (k). If k > 1, the second triangle is an enlargement; if k < 1, it is a reduction.

Key Relationships

Scale Factor

Ratio of any corresponding pair of sides.

k = a'/a = b'/b = c'/c

Perimeter Ratio

Perimeters of similar triangles scale by k.

P2 / P1 = k

Area Ratio

Areas of similar triangles scale by k squared.

A2 / A1 = k²

How to Verify Similarity

For two triangles to be similar, all three ratios of corresponding sides must be equal. If the ratios differ, the triangles are not similar and there is no single scale factor. This calculator checks whether the ratios are consistent and reports any discrepancy.

Practical Applications

  • Model building: Scaling blueprints up or down to physical models.
  • Map reading: Converting map distances to real-world distances.
  • Photography: Understanding enlargements and reductions.
  • Engineering: Creating scaled prototypes from designs.