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A square is inscribed in a circle. If the area of the circle is 144(pi)cm*squared* --sorry the square root thing isnt showing up. Then the exact perimeter of the square is...

I really don't get how to solve this, but the answer is supposed to somehow be 48V2 cm

  • Calculus -

    Make a sketch.
    Did you notice that the diameter of the circle is the diagonal of the square?
    area of circle = πr^2
    πr^2 = 144π
    r^2 = 144
    r = 12 , so the diameter = 24

    let each side of the square be x
    then x^2 + x^2 = 24^2
    2x^2 = 576
    x^2 = 288
    x = √288 = 12√2

    perimeter = 4x = 4(12√2) = 48√2

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