Question

A rectangle with the largest possible area is inscribed in a semi-circle. Find the ratio of the larger side to the smaller side.

Answer 1

The correct answer is: 2:1.
There are no critical points in the feasible domain.
Since there are no critical points, we need to consider the boundary points.
Now $(\frac{l}{2})^2=b^2=>I=2b$
$\frac{l}{2}=\frac{2}{1}$
Therefore, the ratio of the larger side to the smaller side of the rectangle with the largest possible area inscribed in a semi-circle is 2:1.