Hello, rickymylv!
Please tell me how to solve this problem
The ratio of the area of a square to that of the square drawn on its diagonal is:
. . $\displaystyle (A)\;1:3 \qquad (B)\;3:4 \qquad (C)\;2:3 \qquad (D)\;1:2$ A sketch is essential . . . Code:
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A square with side $\displaystyle s$ has area $\displaystyle s^2.$
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The diagonal $\displaystyle d$ of the square can be found with Pythagorus:
. . $\displaystyle d^2 \:=\:s^2+s^2 \:=\:2s^2 \quad\Rightarrow\quad d \:=\:\sqrt{2}\,s$
The area of the square of side $\displaystyle d$ is: .$\displaystyle \left(\sqrt{2}\,s\right)^2 \;=\;2s^2$
Therefore, the ratio of the two areas is . . .