A wire in the form of a square encloses an area of 144 cm². How much area is enclosed if the same wire is bent in the form of a rectangle of length 16 cm ?

The correct option is 128 cm².

Step 1: Find the side length and perimeter of the square.

We are given that the wire in the form of a square encloses an area of 144 cm².

The formula for the area of a square is:

$\text{Area of square}=\text{side}2$

Substituting the given area:

$\text{side}2=144\text{cm}2$

$\text{side}=\sqrt{144}=12\text{cm}$

The total length of the wire is equal to the perimeter of the square:

$\text{Perimeter of square}=4\times \text{side}=4\times 12\text{cm}=48\text{cm}$

Step 2: Find the breadth of the rectangle.

Since the same wire is bent into the form of a rectangle, the perimeter of the rectangle must equal the total length of the wire (48 cm).

The length ($l$) of the rectangle is given as 16 cm. Let the breadth be $b$.

The formula for the perimeter of a rectangle is:

$\text{Perimeter of rectangle}=2\times (l+b)$

Equating the perimeter to 48 cm:

$2\times (16+b)=48$

$16+b=\frac{48}{2}$

$16+b=24$

$b=24-16=8\text{cm}$

Step 3: Calculate the area enclosed by the rectangle.

Now, we calculate the area of the rectangle using the formula:

$\text{Area of rectangle}=\text{length}\times \text{breadth}$

$\text{Area of rectangle}=16\text{cm}\times 8\text{cm}=128\text{cm}2$

Thus, the area enclosed by the wire when bent into the form of a rectangle is 128 cm².