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A flat square picture represented by the unshaded region in the figure
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29 Jun 2023, 01:25
29 Jun 2023, 01:25
Expert Reply
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Question Stats:
46% (02:34) correct
53% (02:03) wrong based on 13 sessions
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Attachment:
GRe square (5).jpg [ 17.22 KiB | Viewed 676 times ]
A flat square picture represented by the unshaded region in the figure above is mounted in a flat square frame, represented by the shaded region, which has uniform width on all sides. What is the ratio of area of frame to the area of picture?
A. 1 : 3
B. 1 : 2
C. 1 : 1
D. 2 : 1
E. 3 : 1
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Re: A flat square picture represented by the unshaded region in the figure
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16 Jul 2023, 04:20
16 Jul 2023, 04:20
Expert Reply
\(\frac{Area of the frame }{ area of the picture} = \frac{Area of the shaded part}{area of the UNshaded part }= \frac{Area of the square ABCD - Area of the square PQRS}{Area of the square PQRS}\)
Area of the square = \(\frac{1}{2} \times diagonal^2\)
and
Area of the square = \(side ^2\)
Area of square \(ABCD = x^2\)
Area of square \(PQRS = \frac{1}{2}x^2\)
\(\frac{Area of the frame}{area of the picture}\) \(= \dfrac{x^2-\frac{1}{2}x^2}{\frac{1}{2}x^2}=\frac{1}{1}\)
C is the answer
_________________
Area of the square = \(\frac{1}{2} \times diagonal^2\)
and
Area of the square = \(side ^2\)
Area of square \(ABCD = x^2\)
Area of square \(PQRS = \frac{1}{2}x^2\)
\(\frac{Area of the frame}{area of the picture}\) \(= \dfrac{x^2-\frac{1}{2}x^2}{\frac{1}{2}x^2}=\frac{1}{1}\)
C is the answer
_________________
gmatclubot
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