Twelve equal squares are placed to fit in a rectangle of diagonal 5cm. There are three rows containing four squares each. No gaps are left between adjacent squares. What is the area of each square?

Correct Option (3)

Let 'x' represent the side length of each equal square. The problem states that twelve such squares are arranged in a rectangle, forming three rows with four squares in each row. Based on this arrangement:

• The width of the rectangle will be 3 times the side length of a square, i.e., 3x.
• The length of the rectangle will be 4 times the side length of a square, i.e., 4x.

The diagonal of a rectangle is related to its length and width by the Pythagorean theorem: (diagonal)² = (width)² + (length)².

Given that the diagonal of the rectangle is 5 cm, we can substitute the values into the theorem:

5² = (3x)² + (4x)²

25 = 9x² + 16x²

25 = 25x²

x² = 1

Since 'x' is the side length of a square, x² represents the area of each square. Therefore, the area of each square is 1 sq. cm.

Incorrect Options:

The other options represent areas that do not satisfy the geometric conditions specified in the problem. If the area of each square (x²) were different from 1 sq. cm, then substituting that value into the Pythagorean theorem (5² = (3x)² + (4x)²) would not result in a diagonal length of 5 cm. Consequently, these options are inconsistent with the given information.