## 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?

Source | OGQR 2020 |

Type | Problem Solving |

Topic | Geometry |

Sub-Topic | Circle / Square |

Difficulty | Medium – Hard |

### Solution

__Given__

__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__

__To Find__

We need to determine

- The radius, in meters, of the tabletop when all four leaves are up.

__Approach & Working__

__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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