The figure above shows a drop-leaf table. With all four leaves down th

Question

https://gmatclub.com/forum/download/file.php?id=47606 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 2019-04-26_1803.png

EgmatQuantExpert · Accepted Answer

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:
  https://e-gmat.com/blogs/wp-content/uploads/2019/05/99.2.png

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.

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

DavidTutorexamPAL · Answer

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.

Archit3110 · Answer

diagonal of square= √2
and diamater = √2
so when sides are up radius √2/2
IMO B

shaonkarim · Answer

I can't visualize the question.
Please explain with drawing. Thanks

Posted from my mobile device

DavidTutorexamPAL · Answer

Hey  shaonkarim

See the attached drawing.
BD is the diameter of the circle and also the diagonal of the square.
Since the side of the square is 1, then BD is sqrt(2) so the radius is 1/2 * sqrt(2)

Hope this helps!

ScottTargetTestPrep · Answer

We see that when the leaves are fully extended, the diameter of the circle is the diagonal of the square. Since the side of the square is 1, then its diagonal is √2. Therefore, the diameter is also √2, and hence the radius is √2/2.

Answer: B

dcummins · Answer

The sooner you realise the shape is just a square inscribed in a circle, the easier your life becomes.

MHIKER · Answer

Actually, this is a square inscribed in a circle.

We need to figure out the diagonal of the square and half the diagonal will be the radius of the circle.

Side of the Square is  1  so, the diagonal will be  1\sqrt{2}   =    \sqrt{2}

Thus the radius is  \frac{\sqrt{2}}{2}

The answer is B.

ThatDudeKnows · Answer

Ballparking! Yay!

The radius is half of the diagonal of the square.

Is that longer than the side, the same as the side, or shorter than the side? Shorter. Cool, eliminate C, D, and E.
Is it half as long as the side (if it were, then the side and the diagonal would be equal, which they aren't)? Nahhhh. Eliminate A.

Answer choice B.

No math.

ThatDudeKnowsBallparking

adityasuresh · Answer

Diagonal of the square is equal to the diameter of the circle. Since each side of square =1, diagonal = root2*side. 
Now a circle inscribing a square share a relationship wherein, diagonal of the square is equal to diameter of the circle.

The figure above shows a drop-leaf table. With all four leaves down th

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