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08 May 2018, 01:47
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:52) correct
31%
(02:41)
wrong
based on 108
sessions
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A flat rectangular picture, represented by the unshaded region in the figure above, is mounted in a flat rectangular frame, represented by the shaded region. The frame is 1 inch wide on all sides. For what value of x, in inches, is the area of the frame equal to the area of the picture?
A. 4
B. 5
C. 6
D. 7
E. 8
Attachment:
vGqVkd7.jpg [ 7.52 KiB | Viewed 10564 times ]
08 May 2018, 02:06
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Bunuel
We'll show two approaches.
The first relies on using the figure without any calculations.
This is an Alternative approach.
The top and bottom part of the frame each have width x and height 1 so their area is x.
The left and right part of the frame (without the corners) each have width 1 and height x so their area is x.
So the area of the frame is 4x.
Since the picture has height x, for it to have 4x area it must have a width of 4.
Then x = 4 + 2 = 6.
(C) is our answer.
The second is an equation driven, a Precise approach.
The area of the frame is the area of the large rectangle (frame+picture) minus that of the picture.
The area of the picture is the product of its height and width.
Since the frame has width is 1 inch on all sides, the large rectangle has area x*(x+2) = x^2 +2x
The picture has height x and width x - 2 so its area is x*(x-2) = x^2 - 2x.
Then the frame has area x^2 + 2x - (x^2 - 2x) = 4x
So, the two are equal when x^2 - 2x = 4x --> x^2 - 6x = 0 --> x(x - 6) = 0 and x = 6.
(C) is our answer.
28 Jul 2018, 11:28
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Bunuel
The area of the picture is x(x-2)
The area of the frame is x(x+2) - x(x-2)
x(x+2) - x(x-2) = x(x-2)
x(x+2) - 2x(x-2) = 0
x(x+ 2 - 2x + 4) = 0 ------> either x = 0 or x = x = 6
Option C
