Calculator
Model: a / b = c / d
Leave the selected unknown side blank. The tool solves the missing value and verifies the proportion automatically.
Plotly Graph
Submit the calculator to generate a side comparison graph and visualize the scale relationship.
Example Data Table
| Case | Triangle 1 - Side A | Triangle 1 - Side B | Triangle 2 - Side A | Triangle 2 - Side B | Unknown | Solved x |
|---|---|---|---|---|---|---|
| Example 1 | 3 | 4 | 6 | x | Triangle 2 - Side B | 8 |
| Example 2 | 5 | 7.5 | x | 12 | Triangle 2 - Side A | 8 |
| Example 3 | 9 | x | 15 | 20 | Triangle 1 - Side B | 12 |
| Example 4 | x | 10 | 12 | 15 | Triangle 1 - Side A | 8 |
Formula Used
Similar triangles keep matching side ratios equal. This calculator uses: a / b = c / d
If Triangle 1 - Side A is unknown
x = (b × c) / d
If Triangle 1 - Side B is unknown
x = (a × d) / c
If Triangle 2 - Side A is unknown
x = (a × d) / b
If Triangle 2 - Side B is unknown
x = (b × c) / a
The graph compares corresponding sides and highlights the shared scale factor. This is useful for geometry learning, image scaling intuition, and model preprocessing examples.
How to Use This Calculator
- Select the side you want to solve as x.
- Enter the other three corresponding side values.
- Click Find x Now to calculate the missing side.
- Review the solved value, scale factor, and ratio check.
- Inspect the graph to compare matching side lengths visually.
- Use the CSV or PDF buttons to save the result.
Frequently Asked Questions
1) What does this calculator solve?
It solves one missing side in two similar triangles. You provide three known corresponding sides, and the calculator finds x using proportional relationships.
2) When are triangles considered similar?
Triangles are similar when matching angles are equal and corresponding sides share one constant scale factor. That common ratio makes proportional solving possible.
3) Why must all entered values be positive?
Side lengths represent distances. Distances cannot be negative, and zero would break proportional division. Positive values keep the geometry meaningful and the formula valid.
4) What does the scale factor mean?
The scale factor shows how much Triangle 2 changes relative to Triangle 1. A factor of 2 means every matching side in Triangle 2 is twice as long.
5) Why is the cross product check useful?
For valid proportions, a × d must equal b × c. The calculator shows both products so you can confirm the solved proportion stays balanced.
6) Can I use decimals in the inputs?
Yes. The calculator accepts decimal values and returns a precise solved result. This helps with scaled drawings, measurements, and training examples with non-integer dimensions.
7) How does this relate to AI & Machine Learning?
Similarity and scale reasoning appear in computer vision, image resizing, feature mapping, and data augmentation. This calculator gives a simple geometric view of proportional scaling.
8) What do the export buttons save?
They save the current solved case. The exported file includes input sides, the x value, ratio metrics, and scale factors for sharing, checking, or recordkeeping.