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9 October, 17:04

3 by 4 rectangle is inscribed in a circle. what's the circumfrence

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  1. 9 October, 17:33
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    The trick here is the recognize that the diagonal length of the rectangle is the diameter of the circle.

    W = width of rectangle = 4

    L = length of rectangle = 3

    D = diagonal of rectangle

    Using pythagorean theorem, we solve for D.

    W^2 + L^2 = D^2

    (4) ^2 + (3) ^2 = D^2

    16 + 9 = D^2

    25 = D^2

    5 = D or - 5 = D

    Since D is a length, D must be positive. Therefore, D=5.

    D = diagonal of the rectangle = 5

    Since D is also the diameter of the circle AND the diameter of a circle is twice the radius, we have the following equation:

    r = radius of circle = 1/2 D = 1/2 (5) = 2.5

    C = circumference

    C = 2 pi r = 2 pi (2.5) = 5 pi
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