Arrange the following in descending order based on their perimeters:
A. A square with an area of 36 sq. cm.
B. An equilateral triangle with a side of 9 cm.
C. A rectangle with 10 cm as length and 40 sq. cm as area.
D. A circle with radius of 4 cm.

Let's calculate the perimeters.

Figure A:

Area = 36 sq. cm

So, side of the square = $$\sqrt{\ 36}$$ cm = 6 cm

So, perimeter of square = 4(side) = $$6\times\ 4=24$$ cm

Figure B:

Perimeter of equilateral triangle = 3(side) = $$3\times\ 9=27$$ cm

Figure C:

Length of rectangle = 10 cm

Area of rectangle = 40 sq. cm

So, breadth of rectangle = (Area)/(Length) = 40/10 = 4 cm

So, perimeter of rectangle = 2(length + breadth) = $$2\left(10+4\right)\ =\ 28$$ cm

Figure D:

Radius of circle is 4 cm

So, perimeter of circle = $$2\pi\ r=2\times\ \dfrac{22}{7}\times\ 4=25.14$$ cm

So, clearly we can see: C>B>D>A is the descending order