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A rectangular picture is surrounded by a boarder, as shown

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A rectangular picture is surrounded by a boarder, as shown [#permalink] New post 17 Aug 2010, 17:21
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Rectangular.jpg
Rectangular.jpg [ 11.23 KiB | Viewed 1553 times ]
A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder?

A. 10
B. 15
C. 30
D. 40
E. 60
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Jul 2013, 01:59, edited 1 time in total.
Renamed the topic, edited the question, added the OA and the image.
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Re: Determining Area [#permalink] New post 17 Aug 2010, 17:54
kwhitejr wrote:
FIGURE: Imagine a rectangle within a rectangle. Every side of the interior rectangle is 2 inches from the congruous side of the larger rectangle.

A rectangular picture is surrounded by a border, as shown in the figure above. Without the border the length of the picture is twice the width. If the area of the border is 196 square inches, what is the length, in inches, of the picture, excluding the border?

A. 10
B. 15
C. 30
D. 40
E. 60


Answer : 30.

Length of the outer rectangle - L, Breadth of the outer rectangle - B.
Length of the inner rectangle - l, Breadth of the inner rectangle - b.

Now given that - L*B = 196 sq. unit and l = 2b.

Also l = L - 4 and b = B - 4

Hence area of the outer rectangle (border area) = 196 - Area of the inner rectangle

(L * B) = 196 - (l*b)

((l+4) * (b+4)) = 196 - (l*b)

Simplifying => (lb + 4l + 4b + 16) = (196 - lb)

(4l + 4b) = 180
(4(2b) + 4b) = 180
12b = 180

b = 15, l = 30.

Hence the length of the inner rectangle or picture is 30 units. Answer C.
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Re: Determining Area [#permalink] New post 17 Aug 2010, 18:15
Ans : C

Assume the length of inner rectangle as L and the width as w then L = 2W
so the length of outer rectange will be L+4 and width as W+4

The area of border is
area of outer rectangle - area of inner rectangle
[(L+4)*(W+4)]- [ L * W] =196

4L +4W +16 = 196
substituting L = 2W we get
12W = 180
W= 15
L = 2W = 30
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Re: Determining Area [#permalink] New post 25 Jul 2013, 01:55
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How to attach a picture to the first post?
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Re: Determining Area [#permalink] New post 25 Jul 2013, 02:00
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink] New post 26 Jul 2013, 22:37
In border area there are 4 square , two simillar rectangle and two another similar rectangle
L= length of inner rectangle, l= width of inner rectangle
Given L= 2l ,
Border area 196= 4 square ( 2*2) + 2 rectangle (2*l)+ 2 rectangle (2*L)
196= 16+ 2*L+ 2*L + L/2*2+L/2*2
180=6L
L= 30.
Hope the approach is correct
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink] New post 29 Oct 2013, 02:02
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Please refer fig below:
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Re: A rectangular picture is surrounded by a boarder, as shown   [#permalink] 29 Oct 2013, 02:02
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