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. 11:14

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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​

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Cora 1 month 2021-09-21T23:33:06+00:00 1 Answer 0 views 0

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    2021-09-21T23:34:53+00:00

    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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