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The diagonal of a square is \( \Large \Large 4\sqrt{2} \) cm. The diagonal of another square whose area is double that of the first square is
A) 8 cm
B) \( \Large 8\sqrt{2} \)cm
C) \( \Large 4\sqrt{2} \)cm
D) 6 cm
Correct answer:
A) 8 cm
Description for Correct answer:
Diagonal of square = \( \Large \sqrt{2} a \) [a = side] .
\( \Large 4\sqrt{2} \)=\( \Large \sqrt{2} a \)
a = 4 cm
Now, area of square = \( \Large a^{2} \)=\( \Large (4)^{2} \)=16
Side of a square whose area is \( \Large 2\times 16 \)
\( \Large a^{2}_{1} \)=32 => \( \Large a_{1}=\sqrt{32} \) => \( \Large a_{1}= 4\sqrt{2} \)
Now, diagonal of new square
= \( \Large \sqrt{2} a \)=\( \Large \sqrt{2}\times 4\sqrt{2} \)=8 cm
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