(a) there is a rectangular frame of wir measuring `20 cm xx 13 cm`. Calculate (i) the perimeter of the square and (ii) radius of the circle, which will have the same perimeter as the rectangular frame, (b) shown that of the three, the circle has the maximum surface area.

Explanation

(a) Perimeter of the rectangular frame
`=(20+13)2 = 66 cm`
Let l be the side of the square and r be the radius of the square having the same perimeter as that of rectangular frame.
(i) for square,
the perimeter of square = 4l = 66 cm
or, `l=66//4 =16.5 cm`
(ii) for circle,
the perimeter of circle = `2 pi r = 66`
or `r=66/(2 pi) = (66)/( 2 xx 22//7) = 10.5 cm`
(b) Area of rectangle = `20 xx 13 = 260 sq` cm.
Area of square = `16.5 xx 16.5 = 272.25 `sq cm,
Area of circle =` pi r^(2) = 22/7 xx (10.5)^(2)`
`=346.5 sq.cm`
Hence out of the three, circle encloses the maximum area.