Discussion
The diagonal of a square is \(5\sqrt{2}\) cm. The diagonal of another square whose area is double that of the first square is:
Answer: B
The diagonal is 10 cm.
A square with diagonal d has area d2/2. The first square has d = 5√2, so its area is 25. The second has area 50, so its diagonal satisfies d2/2 = 50.
\[ d^{2}=100 \Rightarrow d=10\text{ cm} \]
12, 8 and 7 cm would give areas of 72, 32 and 24.5, none of which is 50.
When the area doubles, the side grows by a factor of root 2, and so does the diagonal. The first diagonal is 5√2, so the new one is 5√2 × √2 = 10 cm. This is a quick way to check the answer.
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