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

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

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New post 22 Mar 2019, 01:02
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

100% (02:29) correct 0% (00:00) wrong based on 13 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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Re: Square EFGH is inside the square ABCD so that each side of EFGH can be  [#permalink]

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New post 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
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Re: Square EFGH is inside the square ABCD so that each side of EFGH can be  [#permalink]

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

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