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16 Apr 2021, 05:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:46) correct
33%
(03:07)
wrong
based on 91
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A photograph rectangular in shape is surrounded by a border that is 2 centimeters wide on each side. The combined area of the photograph and the border is a square centimeters . Had the border been 4 centimeters wide on each side, the total area would have been (a + 100) square centimeters. What is the perimeter, in centimeters, of the photograph?
(A) 18
(B) 20
(C) 24
(D) 26
(E) 52
(A) 18
(B) 20
(C) 24
(D) 26
(E) 52
23 Apr 2021, 22:33
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Bunuel
Please look at the figure below :
The green area is the border
Attachment:
GMAT photograph.png [ 7.1 KiB | Viewed 4286 times ]
The length of the photograph is \(a\) and width is \(b\).
Hence perimeter will be \(2(a+b)\)
When the border is \(2\) cms :
The combined length becomes \(a+4\) and combined width becomes \(b+4\)
Hence area
\((a+4 )(b+4) =a\)
\(ab +4a +4b+16 =a (i)\)
When the border is \(4\) cms :
The combined length becomes \(a+8\) and combined width becomes \(b+8\)
Hence area:
\((a+8 )(b+8 ) =( a+100)\)
\(ab+8a+8b+64 = a+100 (ii)\)
\((ii)-(i) \)
\(4a+4b +48=100\)
\(4a+4b=52\)
\(a+b=13\)
\(2(a+b)=26 =\) Perimeter
Ans=D
Hope it's clear.
24 Apr 2021, 14:10
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Bunuel
To summarize, increasing the border by 4 centimeters would increase the total area by 100 square centimeters. (We increase by 2 cm on both sides so the total increase is 4 cm)
Let the current length and width be \(l\) and \(w\).
\((l + 4)(w + 4) = lw + 100\)
\(4L + 4W + 16 = 100\)
\(4L + 4W = 84\)
\(2L + 2W = 42\).
We want the perimeter of the photograph however, so we want \(2(L - 4) + 2(W - 4) = 2L + 2W - 16 = 42 - 16 = 26\).
Ans: D
