Question:
Find the area and perimeter of a square plot of land whose diagonal is $24 \mathrm{~m}$ long. [Take $\sqrt{2}=1.41$ ]
Solution:
Area of the square $=\frac{1}{2} \times$ Diagonal $^{2}$
$=\frac{1}{2} \times 24 \times 24$
$=288 \mathrm{~m}^{2}$
Now, let the side of the square be x m.
Thus, we have:
Area $=$ Side $^{2}$
$\Rightarrow 288=x^{2}$
$\Rightarrow x=12 \sqrt{2}$
$\Rightarrow x=16.92$
Perimeter $=4 \times$ Side
$=4 \times 16.92$
$=67.68 \mathrm{~m}$
Thus, the perimeter of the square plot is 67.68 m.
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