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# Square EFGH is inside the square ABCD so that each side of EFGH can be

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Math Expert
Joined: 02 Sep 2009
Posts: 59725
Square EFGH is inside the square ABCD so that each side of EFGH can be  [#permalink]

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22 Mar 2019, 01:02
00:00

Difficulty:

15% (low)

Question Stats:

95% (02:25) correct 5% (01:16) wrong based on 19 sessions

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Square EFGH is inside the square ABCD so that each side of EFGH can be extended to pass through a vertex of ABCD. Square ABCD\$ has side length $$\sqrt{50}$$ and BE = 1. What is the area of the inner square EFGH ?

(A) 25
(B) 32
(C) 36
(D) 40
(E) 42

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2005_12A_AMC-7b.png [ 10.9 KiB | Viewed 757 times ]

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Manager
Joined: 31 Jul 2017
Posts: 87
Location: India
Schools: Anderson '21, LBS '21
Re: Square EFGH is inside the square ABCD so that each side of EFGH can be  [#permalink]

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22 Mar 2019, 01:23
Since EFGH is a square , DGH= HGF=90

In DGA triangle $$DA^2$$=$$DG^2$$+$$DA^2$$
50= 1 + $$(x+1)^2$$
x+1=7
x=6

So the area of the EFGH = $$x^2$$= 36
Senior Manager
Joined: 25 Feb 2019
Posts: 335
Re: Square EFGH is inside the square ABCD so that each side of EFGH can be  [#permalink]

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22 Mar 2019, 01:43
IMO C .

apply pythagoras theoram in triangle AHB

we get x = 6
hence the area 36

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Re: Square EFGH is inside the square ABCD so that each side of EFGH can be   [#permalink] 22 Mar 2019, 01:43
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