Triangle Scale Factor Calculator
Calculate scale factors between similar triangles and find missing sides
Scale Factor Calculator
Triangle ABC (Original)
Triangle DEF (Scaled)
Example Calculations
Example 1: Finding Scale Factor
Triangle ABC: AB = 3, BC = 4, AC = 5
Triangle DEF: DE = 6, EF = 8, DF = 10
Scale Factor: k = DE/AB = 6/3 = 2
Verification: EF/BC = 8/4 = 2, DF/AC = 10/5 = 2
Result: Scale factor = 2 (enlargement)
Example 2: Finding Missing Sides
Triangle ABC: AB = 6, BC = 8, AC = 10
Given: DE = 3 (corresponding to AB)
Scale Factor: k = DE/AB = 3/6 = 0.5
Missing Sides: EF = BC × k = 8 × 0.5 = 4
DF = AC × k = 10 × 0.5 = 5
Result: Triangle DEF has sides 3, 4, 5 (reduction)
Scale Factor Concepts
Scale Factor > 1
Enlargement - Triangle gets bigger
Scale Factor < 1
Reduction - Triangle gets smaller
Scale Factor = 1
Congruent - Same size triangles
Key Formulas
Scale Factor
k = side₂ ÷ side₁
Area Ratio
Area₂ ÷ Area₁ = k²
Perimeter Ratio
Perimeter₂ ÷ Perimeter₁ = k
Similarity
All side ratios must be equal
Understanding Triangle Scale Factors
What is a Scale Factor?
A scale factor is the ratio between corresponding sides of similar triangles. It tells us how much one triangle has been enlarged or reduced compared to another. If triangles are similar, all corresponding sides have the same ratio.
Applications
- •Architecture and engineering drawings
- •Map scaling and geographic representations
- •Computer graphics and image scaling
- •Proportional reasoning in mathematics
Step-by-Step Method
To find scale factor:
1. Identify corresponding sides
2. Calculate ratios: side₂ ÷ side₁
3. Check if all ratios are equal
4. If equal, triangles are similar
5. The common ratio is the scale factor
Important: For triangles to be similar, all corresponding side ratios must be exactly equal. Even small differences indicate the triangles are not similar.