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26 Apr 2019, 07:05
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
74% (01:28) correct
26%
(01:39)
wrong
based on 2023
sessions
History
Date
Time
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Not Attempted Yet
The figure above shows a drop-leaf table. With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle. What is the radius, in meters, of the tabletop when all four leaves are up?
A. 1/2
B. \(\frac{\sqrt{2}}{2}\)
C. 1
D. \(\sqrt{2}\)
E. 2
PS26602.01
Quantitative Review 2020 NEW QUESTION
Attachment:
2019-04-26_1803.png [ 9.81 KiB | Viewed 27070 times ]
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23 May 2019, 06:41
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Solution
Given
In this question, we are given
- • The figure of a drop-leaf table.
• With all four leaves down the tabletop is a square, and with all four leaves up the tabletop is a circle.
To Find
We need to determine
- • The radius, in meters, of the tabletop when all four leaves are up.
Approach & Working
When all four leaves are up, the table will look like the following:
In this case, the diameter of the circle is equal to the diagonal of the table.
- • As the square table has a side length of 1m, its diagonal will be √2 m.
• Hence, diameter of the circular table = √2 m.
• Therefore, radius of the table = (√2)/2 m
Hence, the correct answer is option B.
General Discussion
26 Apr 2019, 12:38
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Bunuel
We can use simple geometric rules to solve this problem, a Precise approach.
The radius of the circle is half its diameter. Since the diameter of the circle is just the diagonal of the (square) tabletop, and since the diagonal of a square with a side of 1 is sqrt(2) (remember your 45-45-90 triangle!), then our answer is 1/2 * sqrt(2).
(B) is our answer.
