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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # A rectangular picture is surrounded by a boarder, as shown in the  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Joined: 04 Aug 2010 Posts: 13 A rectangular picture is surrounded by a boarder, as shown in the [#permalink] ### Show Tags Updated on: 11 Feb 2018, 21:23 1 5 00:00 Difficulty: 45% (medium) Question Stats: 72% (02:23) correct 28% (02:46) wrong based on 232 sessions ### HideShow timer Statistics 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 Attachment: Rectangular.jpg [ 11.23 KiB | Viewed 10528 times ] Originally posted by kwhitejr on 17 Aug 2010, 17:21. Last edited by Bunuel on 11 Feb 2018, 21:23, edited 2 times in total. Renamed the topic, edited the question, added the OA and the image. Senior Manager Status: Time to step up the tempo Joined: 24 Jun 2010 Posts: 363 Location: Milky way Schools: ISB, Tepper - CMU, Chicago Booth, LSB Re: A rectangular picture is surrounded by a boarder, as shown in the [#permalink] ### Show Tags 17 Aug 2010, 17:54 1 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. _________________ Support GMAT Club by putting a GMAT Club badge on your blog Intern Joined: 11 Aug 2010 Posts: 22 Schools: SUNY at Stonyb Brook WE 1: 4 yrs Re: A rectangular picture is surrounded by a boarder, as shown in the [#permalink] ### Show Tags 17 Aug 2010, 18:15 1 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 _________________ Consider giving Kudos if my post helped you in some way Intern Joined: 12 Aug 2012 Posts: 6 Re: A rectangular picture is surrounded by a boarder, as shown in the [#permalink] ### Show Tags 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 Regards, SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1825 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: A rectangular picture is surrounded by a boarder, as shown in the [#permalink] ### Show Tags 29 Oct 2013, 02:02 6 Please refer fig below: Attachments Rectangular.jpg [ 21.25 KiB | Viewed 9371 times ] _________________ Kindly press "+1 Kudos" to appreciate EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13087 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A rectangular picture is surrounded by a boarder, as shown in the [#permalink] ### Show Tags 03 Jun 2015, 14:48 Hi All, Many Test Takers would use an algebraic approach to solving this problem (which is fine). Since the prompt asks for the length of the picture and the answer are NUMBERS, we can TEST THE ANSWERS. We're given some facts to work with: 1) The length of the picture is TWICE its width 2) The area of the BORDER is 196 sq. inches 3) The border "adds 4" to the length and width of the picture We're asked for the LENGTH of the picture. Since the Length is TWICE the width, chances are that we're looking for an answer that is TWICE another answer (which means either 30 & 15 or 60 & 30). Let's TEST Answer C: 30 IF..... Length = 30 Width = 15 Area of picture = 450 Total Length = 34 Total Width = 19 Total area = 646 Total area - picture area = 646 - 450 = 196. This is a MATCH for what we were told, so this MUST be the answer. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: A rectangular picture is surrounded by a boarder, as shown in the  [#permalink]

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03 Jun 2015, 20:26
2
kwhitejr wrote:
Attachment:
Rectangular.jpg
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

Here is a 20 second estimation method:
Say the width of the picture is b.

Area of the frame can be approximated to 2*b + 2*b + 2*2b + 2*2b = 12b. Some area is left out here. Ignore it.
12b is a bit less than 196 so b would be more than 10 but less than 20. So length is more than 20 but less than 40.
The only option is (C)

Alternatively, if you want to find the exact value, the area of the left out region is 4 squares of 2*2 i.e. 16 square inches.
So 12b = 196 - 16 = 180
b = 15
So length = 30
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Re: A rectangular picture is surrounded by a boarder, as shown in the  [#permalink]

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03 Jun 2015, 23:37
C
(l+4) (b+4) - lb = 196
l+b = 45
if l=2b then b=15 and l=30
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Re: A rectangular picture is surrounded by a boarder, as shown in the  [#permalink]

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07 Jun 2015, 02:47
VeritasPrepKarishma wrote:
kwhitejr wrote:
Attachment:
Rectangular.jpg
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

Here is a 20 second estimation method:
Say the width of the picture is b.

Area of the frame can be approximated to 2*b + 2*b + 2*2b + 2*2b = 12b. Some area is left out here. Ignore it.
12b is a bit less than 196 so b would be more than 10 but less than 20. So length is more than 20 but less than 40.
The only option is (C)

Alternatively, if you want to find the exact value, the area of the left out region is 4 squares of 2*2 i.e. 16 square inches.
So 12b = 196 - 16 = 180
b = 15
So length = 30

Hi karishma,

I did not understand how you can approximate area of the frame as 2*b + 2*b + 2*2b + 2*2b = 12b.
Can you please explain this in detail.
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Re: A rectangular picture is surrounded by a boarder, as shown in the  [#permalink]

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08 Jun 2015, 06:56
1
akhil911 wrote:
VeritasPrepKarishma wrote:
kwhitejr wrote:
Attachment:
The attachment Rectangular.jpg is no longer available
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

Here is a 20 second estimation method:
Say the width of the picture is b.

Area of the frame can be approximated to 2*b + 2*b + 2*2b + 2*2b = 12b. Some area is left out here. Ignore it.
12b is a bit less than 196 so b would be more than 10 but less than 20. So length is more than 20 but less than 40.
The only option is (C)

Alternatively, if you want to find the exact value, the area of the left out region is 4 squares of 2*2 i.e. 16 square inches.
So 12b = 196 - 16 = 180
b = 15
So length = 30

Hi karishma,

I did not understand how you can approximate area of the frame as 2*b + 2*b + 2*2b + 2*2b = 12b.
Can you please explain this in detail.

Attachment:

Approx Area.jpg [ 332.5 KiB | Viewed 7333 times ]

The shaded region is approximately 2b + 2b + 4b + 4b. The four little squares (with question marks) is the only area unaccounted for.
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Re: A rectangular picture is surrounded by a boarder, as shown in the  [#permalink]

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23 Jun 2015, 05:10
1
Hey,

I started with calculating the area of the frame.

The small corners (red rectangles): We know that the frame is 2 wide from every side. So each of the red rectangles will have an area of 2^2 = 4. We have four of those, so 4*4 = 16.

The green rectangles: 2*2w = 4w. We have two of those, so 2*4w = 8w.

The black (remaining two rectangles): 2*w = 2w. We have two of those, so 2*2w = 4w.

Adding the different areas gives as the total frame area: 16 + 12w

From the stem we know that 16 + 12w = 196.

So, w = 15 and the length is 30.
Attachments

frame.png [ 5.87 KiB | Viewed 7147 times ]

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Re: A rectangular picture is surrounded by a boarder, as shown in the  [#permalink]

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06 Oct 2018, 12:10
kwhitejr wrote:

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

Attachment:
Rectangular.jpg

Let $$x$$ be the width and $$2x$$ the length of the photo.
Therefore, the width of the frame is $$x+4$$ and the length is $$2x+4$$

Area of Frame & Photo - Area of Photo = Area of Frame
$$(2x+4)*(x+4)-2x^2=196$$
$$2x(x+4)+4(x+4)-2x^2=196$$
$$2x^2+8x+4x+16-2x^2=196$$
$$12x=196-16$$
$$12x=180$$
$$x=\frac{180}{12}$$
$$x=15$$

Length of the photo $$= 2x = 30 inches$$
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Re: A rectangular picture is surrounded by a boarder, as shown in the &nbs [#permalink] 06 Oct 2018, 12:10
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