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# A photograph, rectangular in shape, is surrounded by a border of 3 cen

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
A photograph, rectangular in shape, is surrounded by a border of 3 cen  [#permalink]

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16 Oct 2018, 00:17
00:00

Difficulty:

35% (medium)

Question Stats:

82% (03:05) correct 18% (02:41) wrong based on 14 sessions

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A photograph, rectangular in shape, is surrounded by a border of 3 centimeters, as shown in the figure below. Without the border, the length of the photograph is twice its width. If the area of the border is 216 square centimeters, what is the width, in centimeters, of the photograph, excluding the border?

(A) 10
(B) 20
(C) 30
(D) 40
(E) 50

Attachment:

2018-10-16_1215.png [ 3.96 KiB | Viewed 317 times ]

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Joined: 26 Feb 2017
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Re: A photograph, rectangular in shape, is surrounded by a border of 3 cen  [#permalink]

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16 Oct 2018, 00:37
1
Area of the border is 216 sq cm
Area of the border = Area of photograph with border - Area of photogragh
As border is 3 cm so length and width will be l+6 , w+6 assuming l is the length and w is the width of the photograph
Also given l = 2w of the photograph
Therefore, (l+6) * (w+6) - l*w = 216
lw +6l+6w+36 -lw = 216
6l +6w = 180
l + w = 30
2w + w = 30
3w = 30
w = 10 cm
Option A is the correct answer

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Re: A photograph, rectangular in shape, is surrounded by a border of 3 cen  [#permalink]

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16 Oct 2018, 00:42
First off, we are given that the border is of uniform width of 3 centimeters. We will use this when algebraically representing the area of the entire depicted figure (photograph w/ border). Note that the width of 3 must be multiplied by 2 to calculate the total width of the entire figure

Next, we are given that the length of the photograph is twice the width (width = w; length = 2w). Using these variables, the area of the photograph = $$2w*w$$ = $$2w^2$$

Finally, we are given the area of the border (216 sq. centimeters)

We will combine all of this information into algebra starting with the area of the entire combined photograph and border (2w+6)(w+6), subtracting the area of the photograph, leaving us with the area of the border (which we know is 216). Calculations are as follows:

$$(2w+6)(w+6)-2w^2=216$$
$$2w^2+18w+36-2w^2=216$$
$$18w+36=216$$
$$18w=180$$
$$w=10$$

Re: A photograph, rectangular in shape, is surrounded by a border of 3 cen   [#permalink] 16 Oct 2018, 00:42
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