Square Inscribed and Circumscribed

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Sun Mar 07, 2010 2:09 pm

What is the ratio of the area of a square that circumscribes a circle to
the area of a square that inscribes the same circle?

(a) sqrt2
(b) sqrt3
(c) 2
(d) sqrt 6
(e) 3

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Source: Beat The GMAT — Problem Solving | Sun Mar 07, 2010 2:09 pm

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Mon Mar 08, 2010 1:22 am

dtweah wrote:What is the ratio of the area of a square that circumscribes a circle to
the area of a square that inscribes the same circle?

(a) sqrt2
(b) sqrt3
(c) 2
(d) sqrt 6
(e) 3

imo c
let the dia of circle=d

the area of outer square=d^2[ side of sq=dia of circle]
the area of inner sq=d^2/2[dia of circle=diagonal of inner sq----> sq of diagonal=2a^2--->a^2=d^2/2]

ratio=d^2/[d^2/2]=2

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