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## OGQR 2020: Question No. 99

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?

### 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.

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