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

Let 's' be the side length of each equal square. The rectangle has 3 rows and 4 columns of squares. Therefore, the width of the rectangle is 4s. The height of the rectangle is 3s.

The diagonal of a rectangle can be found using the Pythagorean theorem: diagonal^2 = width^2 + height^2. We are given that the diagonal is 5 cm. So, 5^2 = (4s)^2 + (3s)^2 25 = 16s^2 + 9s^2 25 = 25s^2 s^2 = 25 / 25 s^2 = 1

The area of each square is s^2. Thus, the area of each square is 1 sq. cm.

Analyzing the options: A) (5)/(7)sq.cm - Incorrect. This value does not match our calculation. B) (5)/(8)sq.cm - Incorrect. This value does not match our calculation. C) 1 sq. cm - Correct. Our calculation shows the area of each square is 1 sq. cm. D) (25)/(12)sq.cm - Incorrect. This value does not match our calculation.

The final answer is C.