Given the perimeter of a rectangle, show that its diagonal is minimum when it is a square

Find the perimeter of a square, if its diagonal is 10sqrt(2)cm .

If the perimeter of a rectangle is contant, then show that the rectangle becomes a square, when its area is maximum.

The perimeter of a rectangle is 28 metres and its diagonal is 10 metres. What are the lengths of its sides?

The perimeter of a rectangle is 42 metres and its diagonal is 15 metres. What are the lengths of its sides?

Find perimeter of a square if its diagonal is 10 sqrt 2cm .

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

ABCD is a rectangle in which diagonal BD bisects /_B. Show that ABCD is a square.

The perimeter of a rectangle is 28 cm and its length is 8cm. Find its: (i) breadth (ii) area (iii) diagonal