ABCD is a square. Equilateral triangles ACF and ABE are drawn on the the diagonal AC and side AB respectively. Find area of △ACF : area of △ABE.
Let AB be a units long.
We know that diagonal of a square = √2× side length
Now, △ ABE and △ ACF are equilateral triangles.
Each angle of both △ ABE and △ ACF is 60∘.
∴△ABE∼△ ACF (by AAA similarity criterion)