Question

If the diagonal of a square is $2\sqrt{2}$ units, then the perimeter of square is:

• A. $8\sqrt{2}$ units
• B. $8$ units
• C. $4$ units
• D. $4\sqrt{2}$ units

Answer 1

The correct option is B $8$ units

Given, the diagonal of the square $=2\sqrt{2}$ units
Let, the side of the square is $a$ units.
Using pythagorean theorem in $△QRS,$ we get
$Q{S}^2=Q{R}^2+R{S}^2$
$\Rightarrow (2\sqrt{2}{)}^2=a^2+a^2\Rightarrow 2^2\times (\sqrt{2}{)}^2=2a^2\Rightarrow 4\times 2=2a^2\Rightarrow 8=2a^2$
Dividing both sides by 2
$\Rightarrow \frac{8}{2}=\frac{2a^2}{2}$
$\Rightarrow 4=a^2$
Taking square root both sides, we get
$\Rightarrow \sqrt{4}=\sqrt{a^2}$
$\Rightarrow \pm 2=a$
$\Rightarrow a=\pm 2$
$\Rightarrow a=2(\because \text{A side of a square cannot be negative}$
$\therefore a=-2\text{is rejected})$

$\therefore$ The perimeter of the square
$=4\times a=4\times 2$
$=8$ units

Hence, option (b.) is the correct choice.