Question

Peter wants to carpet a square room of area $169$ square feet. The length of the side of the room is .

Answer 1

$\underset{–}{\text{Given:}}$
Area of the square room $=169$ square feet.

$\underset{–}{\text{Need to Find:}}$
Length of the side of the room

Let the length of the side of the square room $=l$

Hence,
Area of the square room $=l^2$

$\Rightarrow 169\text{square feet}=l^2$

$\Rightarrow l^2=169\text{square feet}$

$\Rightarrow l=\sqrt{169\text{square feet}}$

Now, as we know that $169=13\times 13={13}^2\therefore \sqrt{169}=\sqrt{{13}^2}=({13}^2{)}^{\frac{1}{2}}={13}^{2\times \frac{1}{2}}(\because (a^m{)}^n=a^{m\times n})={13}^1=13$

$\Rightarrow l=\sqrt{169\text{square feet}}=13\text{feet}$

Therefore, the length of the side of the square room is $\underset{–}{13\text{feet}}$.