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The shaded region in the figure above represents a rectangular frame

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The shaded region in the figure above represents a rectangular frame  [#permalink]

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New post 12 Sep 2018, 01:00
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  35% (medium)

Question Stats:

83% (02:12) correct 17% (01:44) wrong based on 21 sessions

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The shaded region in the figure above represents a rectangular frame with a length of 20 inches and a width of 16 inches. The frame encloses a rectangular picture that has same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?


A. \(5\sqrt{2}\)

B. \(\frac{5}{\sqrt{2}}\)

C. \(\frac{10}{\sqrt{2}}\)

D. 10

E. \(10\sqrt{2}\)


Attachment:
image019.gif
image019.gif [ 2.55 KiB | Viewed 523 times ]

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Re: The shaded region in the figure above represents a rectangular frame  [#permalink]

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New post 12 Sep 2018, 02:25
Bunuel wrote:
Image
The shaded region in the figure above represents a rectangular frame with a length of 20 inches and a width of 16 inches. The frame encloses a rectangular picture that has same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?


A. \(5\sqrt{2}\)

B. \(\frac{5}{\sqrt{2}}\)

C. \(\frac{10}{\sqrt{2}}\)

D. 10

E. \(10\sqrt{2}\)


Attachment:
image019.gif


Given, Area of frame =Area of picture
Area of frame =Area of bigger rectangular region - Area of picture
Or, Area of picture =1/2*20*16=160

Let l and w are the length and width of picture respectively.
Given l:w=20:16=5:4
Or, w=(4/5)*l

So area of picture=l*(4/5)*l=160
Or, \(l^2\)=200
Or, l=10\(\sqrt{2}\)

Ans. (E)
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Re: The shaded region in the figure above represents a rectangular frame  [#permalink]

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New post 14 Sep 2018, 13:01
Bunuel wrote:
Image
The shaded region in the figure above represents a rectangular frame with a length of 20 inches and a width of 16 inches. The frame encloses a rectangular picture that has same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?


A. \(5\sqrt{2}\)

B. \(\frac{5}{\sqrt{2}}\)

C. \(\frac{10}{\sqrt{2}}\)

D. 10

E. \(10\sqrt{2}\)


Attachment:
image019.gif




Lw=20*16-lw
2lw=20*16=lw=160.

w/l=4/5


substitute l*l=200,

l=10root2.


Option E.
GMAT Club Bot
Re: The shaded region in the figure above represents a rectangular frame   [#permalink] 14 Sep 2018, 13:01
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The shaded region in the figure above represents a rectangular frame

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