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1. The ratio of the area of a square to that of the square drawn on diagonal is :

A. 1 : 1

B. 1 : $\sqrt{2}$

C. 1 : 2

D. 1 : 4

Solution:

\begin{aligned} Required ratio \\ = \frac{a^{2}}{{(\sqrt{2} a)}^{2}} \\ = \frac{a^{2}}{2 a^{2}} \\ = \frac{1}{2} \\ = 1 : 2 \end{aligned}

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