Question

A rectangle has a length of $24$ cm and a breadth of $6$ cm. The area of this rectangle is equal to the area of another square. Find the side of the square.

• A. $14$ cm
• B. $12$ cm
• C. $18$ cm
• D. $16$ cm

Answer 1

The correct option is B $12$ cm

$\underset{–}{\text{Given:}}$
Length of rectangle $\left(l\right)$ $=24$ cm
Breadth of rectangle $\left(b\right)$ $=6$ cm

$\underset{–}{\text{Need to Find:}}$
Side length of the square if the area of given rectangle is equal to the area of the square

Now,
Area of the rectangle $=l\times b=(24\times 6)\text{square cm}=144\text{square cm}$

According to the question, the area of rectangle is equal to the area of some another square.

$\therefore$ Area of square $=144$ square cm

Also, we know that area of a square is the square of its side.

Let the side length of the square $=a$.
$\therefore$ Area of the square $=a^2$

$\Rightarrow a^2=144{\text{cm}}^2$

Taking square root on both the sides, we get

$\Rightarrow (a^2{)}^{\frac{1}{2}}=(144{\text{cm}}^2{)}^{\frac{1}{2}}$

$\Rightarrow (a{)}^{2\times \frac{1}{2}}=(12\text{cm}{)}^{2\times \frac{1}{2}}$

$\Rightarrow a=12$ cm

Hence, the side length of the square is $12$ cm.

$\therefore$ Option (b.) is the correct answer.