Question

Area of a square carpet is 25 sq ft. Find the length of each side.

• A. 5 ft
• B. 1.125 ft
• C. 2.5 ft
• D. 0.5 ft

Answer 1

The correct option is A 5 ft

$\text{Detailed step-by-step solution:}$
Area of the square carpet is $25$ sq ft.
Let the side length of the square be $a.$
So, the area of the square will be $a\times a$ or $a^2.$
Considering the above formula, $a^2=25.$
$\Rightarrow \sqrt{a^2}=\pm \sqrt{25}$ (taking square root on both the sides)
We have considered both +ve and -ve values here. For example, $(+1{)}^2=1$ and $(-1{)}^2=1$. Here, square of $1$ and $-1$ is the same. It means that the square root of $1$ will be both $+1$ and $-1$. Accordingly, we can consider that the square root of any non-negative rational number will be given two possible solutions.
$\Rightarrow \sqrt{a\times a}=\sqrt{5\times 5}$
$\Rightarrow a=\pm 5$
Value of a can be either $+5$ or $-5$.
But the length cannot be a negative value. So, $-5$ cannot be considered.
So, the length of each side is $5$ ft.

So, option C is the correct answer.