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# In the figure, the area of rectangle ABCD is 100. What is the area of

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In the figure, the area of rectangle ABCD is 100. What is the area of  [#permalink]

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09 Oct 2018, 20:56
00:00

Difficulty:

35% (medium)

Question Stats:

78% (02:45) correct 22% (02:18) wrong based on 13 sessions

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In the figure, the area of rectangle ABCD is 100. What is the area of the square EFGH ?

(A) 256
(B) 275
(C) 309
(D) 399
(E) 401

Attachment:

recs.jpg [ 15 KiB | Viewed 349 times ]

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Re: In the figure, the area of rectangle ABCD is 100. What is the area of  [#permalink]

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09 Oct 2018, 22:11
In my opinion it must be Option (E).

Area of rectangle is $$(x+2)(x+3) = x^2+5x+6 = 100$$

So $$x^2+5x = 94$$

Area of square is $$(2x+5)^2 = 4x^2+20x+25$$ =4(x^2+5x)+25

Area = 4*94+25 = 360+16+25=401

Hence Option (E) is our choice.

Best,
G

Bunuel wrote:

In the figure, the area of rectangle ABCD is 100. What is the area of the square EFGH ?

(A) 256
(B) 275
(C) 309
(D) 399
(E) 401

Attachment:
recs.jpg

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Re: In the figure, the area of rectangle ABCD is 100. What is the area of  [#permalink]

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09 Oct 2018, 23:21
If we simplify area of EFGH
=(2x+5)^2
=4(area of ABCD) +1
=4x100 + 1
=401

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Re: In the figure, the area of rectangle ABCD is 100. What is the area of   [#permalink] 09 Oct 2018, 23:21
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