What is the ratio of area of square to that of the square drawn from its diagonal ?

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Solution

If x is the side of square its area = $x^{2}$
The length of its diagonal = $\sqrt{2} x$
Hence, area of square on its diagonal = $2 x^{2}$
Therefore, the ratio of area of square to that square drawn from its diagonal = $\frac{x^{2}}{2 x^{2}} = \frac{1}{2}$

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What is the ratio of area of square to that of the square drawn from its diagonal ?

If x is the side of square its area = x2 The length of its diagonal = √2x Hence, area of square on its diagonal = 2x2 Therefore, the ratio of area of square to that square drawn from its diagonal = x22x2=12

If x is the side of square its area = $x^{2}$
The length of its diagonal = $\sqrt{2} x$
Hence, area of square on its diagonal = $2 x^{2}$
Therefore, the ratio of area of square to that square drawn from its diagonal = $\frac{x^{2}}{2 x^{2}} = \frac{1}{2}$