Calculator
Enter decimals, fractions, or radicals such as 7, 3/2, sqrt(50), or 2*pi.
Example Data Table
| Example | Triangle A | Triangle B | Scale Factor | Area Factor |
|---|---|---|---|---|
| Basic | 6, 8, 10 | 9, 12, 15 | 1.5 | 2.25 |
| Radical Input | sqrt(18), 6, 3*sqrt(2) | 6, 6*sqrt(2), 9 | sqrt(2) | 2 |
| Unknown Solve | x, 4, 5 | 9, 12, 15 | 3 | 9 |
Formula Used
Similar triangles keep matching side ratios equal. If the scale factor from Triangle A to Triangle B is k, then:
a2 / a1 = b2 / b1 = c2 / c1 = k
Perimeters scale by the same factor:
P2 / P1 = k
Areas scale by the square of the factor:
Area2 / Area1 = k²
This calculator uses any valid pair of corresponding measures to find k. Then it solves missing sides, perimeters, and areas while checking consistency.
How to Use This Calculator
Enter names for both triangles if needed. Fill any known corresponding sides. Use optional perimeter or area fields only when they help define the same similarity relationship.
You may enter decimals, fractions, or radicals. After submission, the solved values appear above the form. The page also shows steps, a graph, and export buttons.
If the given values conflict, the calculator stops and reports the mismatch. That helps you verify whether the triangles are actually similar.
FAQs
1. What does this calculator solve?
It solves missing corresponding sides, scale factor, perimeter scaling, and area scaling for similar triangles. It also checks whether your given values agree with similarity.
2. Can I enter radicals like sqrt(50)?
Yes. You can enter expressions such as sqrt(50), 3/2, 2*pi, or mixed arithmetic. The parser evaluates the expression before solving.
3. How is the scale factor found?
The calculator compares any complete corresponding pair. It can also use perimeter ratio or the square root of the area ratio when those are provided.
4. What happens if my values are inconsistent?
You will get an error message. That means at least one ratio does not match the others, so the data does not describe one pair of similar triangles.
5. Do I need all six sides?
No. A consistent scale factor plus enough corresponding information is enough. Unknown sides can be solved after the common ratio is established.
6. Can perimeters and areas help solve the triangles?
Yes. Perimeters scale directly with the factor. Areas scale with the square of the factor. Those relationships can fill missing totals when the ratio is known.
7. What does the graph show?
The graph compares the three solved corresponding sides for both triangles. It helps you visually inspect how the scale factor changes each side.
8. Can I download the results?
Yes. Use the CSV button for spreadsheet style output. Use the PDF button to create a clean downloadable summary of the calculated results.