Question : If the perimeter of a square is $80\;\mathrm{cm}$, then what is the diagonal (in $\mathrm{cm}$) of the square?
Option 1: $20\sqrt{2}$
Option 2: $40\sqrt{2}$
Option 3: $80\sqrt{2}$
Option 4: $20$
Correct Answer: $20\sqrt{2}$
Solution : Let the side length of a square be $ \text{s}\;\mathrm{cm}$. The perimeter of the square $=4 \times \text{s}$ Given that the perimeter is $80\;\mathrm{cm}$. The side length of the square $=\frac{80}{4} = 20\;\mathrm{cm}$ The diagonal of a square $=\sqrt{2} \times \text{s }$ The length of the diagonal of this square $=\sqrt{2} \times 20 = 20\sqrt{2}\;\mathrm{cm}$ Hence, the correct answer is $20\sqrt{2}$.
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