Rectangle inscribed in a semicircle?

Question

Find the rectangle of largest area that can be inscribed in a semicircle of diameter 55, assuming that one side of the rectangle lies on the diameter of the semicircle.
The largest possible area is______

Answer 1

I would say start from the middle of the diameter and draw 3 radius lines two at 45 degrees and one straight up now if you connect the top two points from the 45 degree lines you have two right triangles, so you have hypotenuse value 27.5 and an angle 45 degrees so you can find the other sides.

27.5sin(45)=19.45 = width of rectangle
2(19.45) = 38.89 = length
39.89*19.45= 756.25 = area

Answer 2

Rectangle is within a semi circle of radius r
Let r make angle θ with x axis
L = 2 r cos θ
B = 2 sin θ
A = 4r sin θ cos θ
A = 2r (2 sin θ cos θ)
A = 2r sin 2θ
A = 55 sin 2θ
A max = 55