Given the sum of the perimiter of a square and a circle, show that the sum of their areas is least when the side of the square is equal to radius of the circle.

A farmer wants to construct a circular well and a square garden in his field. He wants to keep sum of their permeters fixed. The prove that the sum of their area is least when the side of a square garden is double the radius of the circular well. Do you think good planning can save energy, time and money.

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

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

The area of a circle is equal to the sum of the areas of the two circles, whose radii are 5 cm and 12 cm respectively. Find the radius of the circle.

Sum of the areas of two squares is 468 m^2 . If the difference of their perimeters is 24 m, find the sides of the two squares.

Area of a square plot is 2304 m^2 . Find the side of the square plot.

A wire of length 20m is to be cut into two pieces. One of the pieces is to be made into a square and other into a circle. What could be the lengths of the two pieces so that the combined area of the square and the circle is minimum ?

A wire of length 25 cm is to be cut into two pieces. One of the pieces is to be made into a square and other into a circle. What would be the length of the two pieces so that the combined area of the square and the circle is minimum ?

A wire of length 36 m is to be cut into two pieces. One of the pieces is to be made into a square and other into a circle. What could be the lengths of the two pieces so that the combined area of the square and the circle is minimum ?