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?

The correct option/answer is 1 sq. cm.

Let the side length of each of the twelve equal squares be represented by $x$ cm.

We are given that twelve equal squares are arranged to fit exactly inside a rectangle in a grid of 3 rows and 4 columns. No gaps are left between the adjacent squares.

Because the squares are arranged in 3 rows and 4 columns, the dimensions of the outer rectangle can be expressed in terms of the side length of the individual squares, $x$:
- The height (or width) of the rectangle, consisting of 3 rows of squares, is $3x$.
- The length of the rectangle, consisting of 4 columns of squares, is $4x$.

The diagonal of this rectangle is given as 5 cm. Using the Pythagorean theorem, the relationship between the sides of a right triangle formed by the length, width, and diagonal of the rectangle is:
${\left(3x\right)}^2+{\left(4x\right)}^2=5^2$

Expanding the squared terms, we get:
$9x^2+16x^2=25$

Combining the like terms on the left side:
$25x^2=25$

Dividing both sides by 25:
$x^2=1$

Since the area of each individual square is given by the formula $\text{Area}=x^2$, we find that:
$\text{Area of each square}=1\text{sq cm}$