Question : If the perimeter of a square is $44\;\mathrm{cm}$, what is the diagonal (in $\mathrm{cm}$) of the square?
Option 1: $11\sqrt{2}$
Option 2: $2\sqrt{11}$
Option 3: $11$
Option 4: $44\sqrt{2}$
Correct Answer: $11\sqrt{2}$
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 $44\;\mathrm{cm}$.
The side length of the square $=\frac{44}{4} = 11\;\mathrm{cm}$
The diagonal of a square $=\sqrt{2} \times \text{s }$
The length of the diagonal of this square $=\sqrt{2} \times 11 = 11\sqrt{2}\;\mathrm{cm}$
Hence, the correct answer is $11\sqrt{2}$.
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