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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? – OGQR 2020 Question #84 with Solution

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?

SourceOGQR 2020
TypeProblem Solving
TopicGeometry
Sub-TopicQuadrilateral
DifficultyMedium – 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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