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
In this question, we are given
- A rectangle of area 24 is partitioned into exactly 3 nonoverlapping squares of equal area.
To Find
We need to determine
- The length of the longest side of the rectangle.
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.
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