Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

Prove that among all the rectangles of the given perimeter, the square has the maximum area.

Prove that among all the rectangles of the given area, square has the least perimeter.

Rectangles are inscribed inside a semi-circle of radius rdot Find the rectangle with maximum area.

A rectangle is inscribed in an equilateral triangle of side length 2a units. The maximum area of this rectangle can be sqrt(3)a^2 (b) (sqrt(3)a^2)/4 a^2 (d) (sqrt(3)a^2)/2

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

Find the dimensions of the largest rectangle that can be inscribed in a semi circle of radius r cm.

A rectangle of the greatest area is inscribed in a trapezium A B C D , one of whose non-parallel sides A B is perpendicular to the base, so that one of the rectangles die lies on the larger base of the trapezium. The base of trapezium are 6cm and 10 cm and A B is 8 cm long. Then the maximum area of the rectangle is 24c m^2 (b) 48c m^2 36c m^2 (d) none of these

Each side of a square has length 4 units and its center is at (3,4). If one of the diagonals is parallel to the line y=x , then anser the following questions. ,brgt The radius of the circle inscribed in the triangle formed by any two vertices of the square and the center is