Maximize the area of the right triangles inscribed in the un

Maximize the area of the right triangles inscribed in the unit semicircle.

Maximize the area of the right triangles inscribed in the unit semicircle.

Solution

Well, the area of a triangle is half the base times the height. T he base will stay the same for us, namely the diameter. So when is the height the greatest? Where the perpendicular bisector of the base strikes the circle, and at that point the area is the square of the radius. so maximum area = 0.5*2*1 = 1 sq.units