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

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Math Expert
Joined: 02 Sep 2009
Posts: 55231
The shaded region in the figure above represents a rectangular frame  [#permalink]

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12 Sep 2018, 01:00
00:00

Difficulty:

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 [ 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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12 Sep 2018, 02:25
Bunuel wrote:

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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Joined: 04 Sep 2015
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Re: The shaded region in the figure above represents a rectangular frame  [#permalink]

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14 Sep 2018, 13:01
Bunuel wrote:

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