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A square mirror has exactly half the area of the rectangular wall on w

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A square mirror has exactly half the area of the rectangular wall on w [#permalink]

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New post 10 Mar 2015, 14:54
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A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 42 inches and the width of the wall is 56 inches, what is the length of the wall, in inches?

(A) 84
(B) 72
(C) 70
(D) 63
(E) 56
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Mar 2015, 04:19, edited 1 time in total.
Added the OA.

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Re: A square mirror has exactly half the area of the rectangular wall on w [#permalink]

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New post 10 Mar 2015, 17:39
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Turkish wrote:
A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 42 inches and the width of the wall is 56 inches, what is the length of the wall, in inches?

(A) 84
(B) 72
(C) 70
(D) 63
(E) 56


Just to be cute and do this without too many calculations, we could factor 42 into 2 * 3 * 7 and 56 into 2 * 2 * 2 * 7.

So the area of the mirror would be (2 * 3 * 7)(2 * 3 * 7), and double the area of the mirror is therefore \(2^3 * 3^2 * 7^2\).

For the wall we already have \(2^3 * 7\) for the width. So the length must be \(3^2 * 7\) = 63

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[Reveal] Spoiler:
D
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Re: A square mirror has exactly half the area of the rectangular wall on w [#permalink]

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New post 11 Mar 2015, 02:04
Since the mirror is 42 inches in all sides, it must be a square. Area of a square is A=a^2; 42^2=1764.Area of rectangle is double of that 2 *1764=3528.Now A=lw and we need find w so A/l=w ; 3528/56= 62 Answer!

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Re: A square mirror has exactly half the area of the rectangular wall on w [#permalink]

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New post 11 Aug 2017, 04:41
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Re: A square mirror has exactly half the area of the rectangular wall on w [#permalink]

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New post 11 Aug 2017, 07:46
2*42*42=56*length
2*42*42= units digit of 8. Answer 63

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Re: A square mirror has exactly half the area of the rectangular wall on w   [#permalink] 11 Aug 2017, 07:46
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