Question

If the perimeter of a circle is equal to that of square ,then find the ratio of their areas .

Answer 1

See the attachment... and plz reply me after u watch this solution...

Answer 2

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

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hope it helps ^_^