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The figure above represents a square photograph bordered by a frame th
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01 Mar 2021, 11:20
01 Mar 2021, 11:20
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GRE The figure above represents a square photograph.jpg [ 7.19 KiB | Viewed 2976 times ]
The figure above represents a square photograph bordered by a frame that has a uniform width of 3 inches. If the frame and the picture have the same area, and each of the photograph's sides measures x inches, which of the following equations is true?
A. \((x+6)^2=2x^2\)
B. \((x+3)^2=2x^2\)
C. \((x+9)^2=2x^2\)
D. \((x+3)^2=4x^2\)
E. \((x+6)^2=4x^2\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: The figure above represents a square photograph bordered by a frame th
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01 Mar 2021, 23:44
01 Mar 2021, 23:44
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Carcass wrote:
Attachment:
GRE The figure above represents a square photograph.jpg
The figure above represents a square photograph bordered by a frame that has a uniform width of 3 inches. If the frame and the picture have the same area, and each of the photograph's sides measures x inches, which of the following equations is true?
A. \((x+6)^2=2x^2\)
B. \((x+3)^2=2x^2\)
C. \((x+9)^2=2x^2\)
D. \((x+3)^2=4x^2\)
E. \((x+6)^2=4x^2\)
Whenever we are given that - The frame and the picture have the same area
Total Area = 2 (Area of picture)
Side of frame (including the picture) = \((x + 6)\)
Area (including the picture) = \((x + 6)^2\)
Side of picture = \(x\)
Area of picture = \(x^2\)
So, \((x + 6)^2 = 2x^2\)
Hence, option A
The figure above represents a square photograph bordered by a frame th
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28 Apr 2021, 06:37
28 Apr 2021, 06:37
1
Alternatively, we can set the area of the picture equal to the area of the entire frame minus the picture.
\(x^2 = (x+6)^2-x^2\)
Adding \(x^2\) to both sides gives
\(2x^2 = (x+6)^2\)
\(x^2 = (x+6)^2-x^2\)
Adding \(x^2\) to both sides gives
\(2x^2 = (x+6)^2\)
