Question

Find the dimensions of the rectangle of greatest area that can be inscribed in a semicircle of radius R.

Answer 1

u look sad lol

Answer 2

I can get part-way. Let the semi-circle be sitting on its diameter.
Inscribe a rectangle of vertical height a, draw radius to the point where
a strikes the circumference. use the triangle of the horizontal radius and a and the sloping radius, so that
a = R sin @
half the base of the rectangle, along the diameter is w/2
(w/2) = R cos @

the area of the rectangle is a w = 2 R^2 sin @ cos @ and I would bet that this
is maximized when @=45o, though I cannot prove it.

area = a w = 2 R^2 (0.707)().707) = R^2. looks good, though speculative

Answer 3

it says rectangle has to be inscribed in a semicircle !!

Answer 4

Opps..my bad

Answer 5

Yeah the rectangle is inside the circle lol

Answer 6

Noooo rectangle must be INscribed, thus wholly within the semicircle.
I do wish I could draw that well, though.