A) \[20\sqrt{2}c{{m}^{2}}/s\]
B) \[10\sqrt{2}c{{m}^{2}}/s\]
C) \[\frac{1}{10\sqrt{2}}c{{m}^{2}}/s\]
D) \[\frac{10}{\sqrt{2}}c{{m}^{2}}/s\]
E) \[5\sqrt{2}\,c{{m}^{2}}/s\]
Correct Answer: B
Solution :
Let D denotes the diagonal of the square. Given, \[\frac{dD}{dt}=0.5\text{ }cm/s\] ... (i) Since, \[A=400=\frac{1}{2}{{D}^{2}}\Rightarrow D=20\sqrt{2}\] As\[A=\frac{{{D}^{2}}}{2}\] On differentiating w.r.t. t, we get \[\frac{dA}{dt}=\frac{d}{dt}\left( \frac{{{D}^{2}}}{2} \right)\] \[=D\frac{dD}{dt}\] \[=20\sqrt{2}\times 0.5\] \[=10\sqrt{2}c{{m}^{2}}/s\]
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