A square divided by three line segments. The red and blue areas are equal. What’s the length proportion a : b?

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## Solution

The proportion a : b is the Golden Ratio φ.

geometry puzzles to train your brain

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- Post author By Rik
- Post date May 10, 2022
- 3 Comments on Check and balance

A square divided by three line segments. The red and blue areas are equal. What’s the length proportion a : b?

Scroll down for a solution to this problem.

The proportion a : b is the Golden Ratio φ.

- Tags area, length, proportion, square

## 3 replies on “Check and balance”

From the solution it is not clear how the coordinates of A and B are determined? Can you please help?

Yes. I now realized how the coordinates of A and B are found out.

For A, it is the intersection of the line passing through (0,1/2) and (1,0) and the line passing through (a,1) and (0,0). Similarly for B.

Very nice method.

Glad you found out. Yeah, it ís a nice application of Cartesian coordinates.