Question

Can a Triangle have 1 right angle and 3 equal sides?

Answer 1

Only if it is a curvilinear triangle.

Explanation:

If an ordinary planar triangle is equilateral (having equal sides), then it will also be equiangular (having equal angles) and those angles will sum to `pi` radians (`180^@`), so each internal angle will be `pi/3` radians (`60^@`).

On the other hand a curvilinear triangle on the surface of a sphere could have `3` right angles and `3` equal sides if the length of each side is `1/4` of the circumference of the sphere.