## OGQR 2020: Question No. 84

If a rectangle of area 24 can be partitioned into exactly 3 nonoverlapping squares of equal area, what is the length of the longest side of the rectangle?

Source | OGQR 2020 |

Type | Problem Solving |

Topic | Geometry |

Sub-Topic | Quadrilateral |

Difficulty | Medium – Hard |

### Solution

__Given__

__Given__

In this question, we are given

- A rectangle of area 24 is partitioned into exactly 3 nonoverlapping squares of equal area.

__To Find__

__To Find__

We need to determine

- The length of the longest side of the rectangle.

__Approach & Working__

__Approach & Working__

As the squares are nonoverlapping, the total area of all 3 squares will be equal to the area of the rectangle.

- Area of each square = 24/3 = 8
- Therefore, side length of each square = √8 = 2√2
- Thus, the longest side of the rectangle = 2√2 + 2√2 + 2√2 = 6√2

Hence, the correct answer is option D.

Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don’t you

try out our FREE Trial?We are themost reviewed online GMAT Preparation company in GMATClubwith more than 2000 reviews as of January 2021.