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Math Help - Another word problem!

  1. #1
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    Another word problem!

    A circle and a square have the same area. Find the length of the diagonal of the square divided by the radius of the circle. (Hint: draw a diagram and label unknowns.)
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  2. #2
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    Quote Originally Posted by lilikoipssn View Post
    A circle and a square have the same area. Find the length of the diagonal of the square divided by the radius of the circle. (Hint: draw a diagram and label unknowns.)

    Since they have the same area we know.

    A=\pi r^2 \mbox{ and } A=s^2 \iff \pi r^2=s^2 \iff r^2=\frac{s^2}{\pi}

    r=\frac{s\sqrt{2}}{\sqrt{\pi}}

    Now using the pythagorean theorem we know the length of the diagonal is

    d^2=s^2+s^2 \iff d^2 =2s^2 \iff d=s\sqrt{2}

    Now we are asked to find the ratio of diagonal to the radius

    \frac{s\sqrt{2}}{\frac{s\sqrt{2}}{\sqrt{\pi}}}=\sq  rt{\pi}
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