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Re: If a square mirror has a 30-inch diagonal, what is the area of the mir [#permalink]

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17 Feb 2016, 04:10

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This post received KUDOS

Bunuel wrote:

If a square mirror has a 30-inch diagonal, what is the area of the mirror, in inches?

A. 225 B. 450 C. 600 D. 750 E. 900

Kudos for correct solution.

Let's name square sides of s, using pythagoras 30^2=s^2+s^2, this ends to s=\sqrt{450}, which is \sqrt{2*3^2*5^2}, hence square sides are 15\sqrt{2}, 15\sqrt{2}*15\sqrt{2}=450, hence, i think the correct answer is B.

*Although \(d = s\sqrt{2}\) probably should be in memory, it is easily derived. Two sides, \(s\), of a square, form a right isosceles triangle. Pythagorean theorem hence yields: \(s^2 + s^2 = d^2\) \(2s^2 = d^2\) \((\sqrt{2})(\sqrt{s^2})=\sqrt{d^2}\) \((\sqrt{2})s = d\), or \(s\sqrt{2}= d\)