In this figure, the shaded area is in between an isosceles triangle with sides 1, 1 and x, and an equilateral triangle with sides x.
If x is close to zero, the isosceles triangle becomes very thin and the shaded area in very small.
If x is close to 1, there is very little difference between the isosceles triangle and the equilateral triangle, and again the shaded area is very small.
In between, the shaded area is at a maximum. For what value of x is this the case?
Usually I like to engineer these puzzles so that the solution is a whole number, however this is not possible in this case, but the exact solution can be expressed quite concisely. A numerical solution is also acceptable to, let’s say, four decimal places.