Question 549014
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5) The ratio of area and perimeter of a square is 2 : 1 , then area of circle with diameter equal to diagonal of square is:


Let the measure of the side of the square be represented by *[tex \Large s].


Then the Area is given by *[tex \Large A\ =\ s^2] and the perimeter by *[tex \Large P\ =\ 4s].  But with the given proportion, *[tex \Large A\ =\ 2P].  Hence *[tex \Large s^2\ =\ 8s] which is to say *[tex \Large s\ =\ 8].


The diagonal of a square with side measure *[tex \Large s] is *[tex \Large s\sqrt{2}], hence the radius of a circle with diameter equal to the diagonal of the square is *[tex \Large \frac{s}{2}\sqrt{2}], in your case, *[tex \Large 4\sqrt{2}].


The area of a circle with radius *[tex \Large r] is *[tex \Large A\ =\ \pi{r}^2].  So in your case: *[tex \Large 32\pi]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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