The sum of the perimeter of a circle and square is k , where k is a constant. Prove that the sum of their areas is least when the side of the square is double the radius of the circle.

If the perimeter of a circle and perimeter of a square are equal, then find the ratio of their arẽas.

Corners of a square are. on a circle. If the length of one side of square is 10 cm, find the perimeter of the circle.

Prove that in any parallelogram, the 'sum of the squares of all sides is equal to the sum of the squares of the diagonals'.

A square is drawn by joining the mid points of the sides of a square. A third square is drawn inside the second square in the same way and the process is continued infinitely. If the side of the square is 10 cms, find the sum of the areas of all the squares so formed.

Find the side of the square whose area and perimeter are numercally equal.

The perimeter of a rectangle is 34cm,area 60square centimeter. Find the sides.

In the figure, semicircles are drawn with the sides of a triangles as diameters. Prove that the area of the largest semicircle is the sum of the areas of the smaller ones.

Algebraic form of an n^(th) term of an arithmetic sequence is 8n-4. Prove that the sum of the n consecutive terms of this sequence is a perfect square.