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# Rectangle ABCD, pictured below, shares 50% of its area with square EFG

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
Rectangle ABCD, pictured below, shares 50% of its area with square EFG  [#permalink]

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29 Mar 2019, 01:51
00:00

Difficulty:

45% (medium)

Question Stats:

62% (02:19) correct 38% (02:48) wrong based on 21 sessions

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Rectangle ABCD, pictured below, shares 50% of its area with square EFGH. Square EFGH shares 20% of its area with rectangle ABCD. What is AB/AD ?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 10

Attachment:

54371c10b04c0bcf5a86491a02c9b7ecf851cb2d.png [ 4.18 KiB | Viewed 393 times ]

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Re: Rectangle ABCD, pictured below, shares 50% of its area with square EFG  [#permalink]

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29 Mar 2019, 03:06
Bunuel wrote:

Rectangle ABCD, pictured below, shares 50% of its area with square EFGH. Square EFGH shares 20% of its area with rectangle ABCD. What is AB/AD ?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 10

Attachment:
54371c10b04c0bcf5a86491a02c9b7ecf851cb2d.png

50% of ABCD = 20% of EFGH

i.e. (1/2) ABCD = (1/5) EFGH

i.e. ABCD = (2/5) EFGH

Let, EF=FG=GH=HE = x
i.e. AB = 2x

i.e. $$2x * AD = (2/5)*x^2$$

i.e. $$AD = x/5$$

i.e. AB/AD = 2x/(x/5) = 10/1

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Re: Rectangle ABCD, pictured below, shares 50% of its area with square EFG  [#permalink]

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29 Mar 2019, 08:49
Bunuel wrote:

Rectangle ABCD, pictured below, shares 50% of its area with square EFGH. Square EFGH shares 20% of its area with rectangle ABCD. What is AB/AD ?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 10

Attachment:
54371c10b04c0bcf5a86491a02c9b7ecf851cb2d.png

let square area = 100
side of square = 10
given 20 % area of square is shared with rectangle ABCD
i.e 20*100/100 = 20
and 50% of rectangle area is shared with EFGH ; so total area of rectangle = 20= x*50/100 ; x = 40
side of square = 10 i.e half way of length of rectangle ; 20 is length and width AD = 2
so ratio ; 20/2 ; 10
IMO E
Re: Rectangle ABCD, pictured below, shares 50% of its area with square EFG   [#permalink] 29 Mar 2019, 08:49
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