A wire of length 20 cm is to be bent into a rectangle. Which of the...

Let the length and breadth of the rectangle be $x$ and $y$ respectively.

Given the perimeter of the rectangle is $20\text{ cm}$.

$2(x + y) = 20 \Rightarrow x + y = 10$

The area of the rectangle is $A = xy$.

Substituting $y = 10 - x$, we get:

$A = x(10 - x) = 10x - x^2$

To find the maximum area, we can complete the square:

$A = 25 - (x - 5)^2$

The maximum value of $A$ is $25\text{ cm}^2$, which occurs when $x = 5\text{ cm}$.

When $x = 5\text{ cm}$, $y = 10 - 5 = 5\text{ cm}$.

Since $x = y$, the rectangle of the largest area is a square. Thus, statement I is correct.

The maximum possible area is $25\text{ cm}^2$. It is not possible to form a rectangle of area $27\text{ cm}^2$. Thus, statement II is incorrect.

Only statement I is correct.

Answer: I only