In the case of a triangle with angle measures of 30â°, 60â°, and 90â° and a hypotenuse length equal to x, what is the perimeter of the triangle in terms of x?

Let "a" be a shorter leg (lies opposite to angle 30°), "b" is a longer leg (lies opposite to angle 60°), "c" is a hypotenuse (c = x).
In the 30°-60°-90° triangle, the side lying opposite to the angle 30° is half the hypotenuse, so:



By the Pythagorean theorem: