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.