Question

A garden is in the shape of square. If its perimeter is $24$ units, then its diagonal length is:

• A. $6\sqrt{2}$ units
• B. $6$ units
• C. $\sqrt{2}$ units
• D. $3\sqrt{2}$ units

Answer 1

The correct option is A $6\sqrt{2}$ units

Let the side of the square be $s.$
Given, the perimeter of the garden = 24 units
We know that, the perimeter of a square $=4\times s$
$\Rightarrow 24=4\times \text{s}(\because \text{given the perimeter is 24})$
Divide both sides by 4
$\Rightarrow \frac{24}{4}=\frac{4\times \text{s}}{4}$
$\Rightarrow 6=\text{s}$
$\Rightarrow \text{s}=6$

Hence, the diagonal of the square $=\sqrt{2}\times \text{s}$
$=\sqrt{2}\times 6$
$=6\sqrt{2}$ units
Hence, option (a.) is the correct choice.