Question

116. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
a. 22:7 c. 7:22
b. 14:11 d. 11:1427​

Answer 1

perimeter of circle = 2π r

perimeter of square = 4a

a = diameter of circle (d)

so,

πd = 4a

ratio of areas,

π r^2 : d^2 (because, a = d) ---------- (1)

r = d/2

substituting, r value in π r^2, we get,

π × (d/2)^2

= π × d^2/4

now, from (1)

π d^2/4 : d^2

so,

π d^2/4 ÷ d^2

= π d^2/4 × 1/d^2 (where, d^2 will get cancelled)

= π/4 × 1 -------- (2)

substituting π value in (2),

= 22/7 ÷ 4

= 22/7 × 1/4

= 22/28 (using 2 as the common divisor, we divide 22 and 28 to get 11 and 14 respectively)

=11/14

therefore, ratio of areas = 11 : 14