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Official Solution:
If the area of square \(A\) is three times the area of square \(B\), what is the ratio of the diagonal of square \(B\) to that of square \(A\)?
A. \(\frac{1}{3^{(\frac{1}{2})}}\)
B. \(\frac{1}{3^{(\frac{1}{3})}}\)
C. \(3^{(\frac{1}{3})}\)
D. \(3^{(\frac{1}{2})}\)
E. 3
The ratio of the diagonals is the same as the ratio of the sides. If the side of \(B\) is \(b\), then the side of \(A\) must be \(\sqrt{3}b\). The required ratio is:
\(\frac{b}{\sqrt{3}b} = \frac{1}{\sqrt{3}} = \frac{1}{3^{\frac{1}{2}}}.\)
Answer: A
Hi,
I answer correctly, but it would help me if you explain in a little more detail the conclusion in order to answer quickly: The ratio of the diagonals is the same as the ratio of the sides. If the side of B is b, then the side of A must be 3√b
Thanks a lot.
Regards,
Luis Navarro
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