A) \[4\sqrt{3}m\]
B) \[5\sqrt{3}m\]
C) \[5\sqrt{2}m\]
D) \[8\,m\]
E) \[6\,m\]
Correct Answer: E
Solution :
Let\[AB=x\text{ }m,\text{ }BC=y\text{ }m\]and\[AC=10\text{ }m\] \[\therefore \] \[{{x}^{2}}+{{y}^{2}}=100\] ...(i) On differentiating w.r.t. r, we get \[2x\frac{dx}{dt}+2y\frac{dy}{dt}=0\] \[\Rightarrow \] \[2x(3)-2y(4)=0\] \[\Rightarrow \] \[x=\frac{4y}{3}\] On putting this value in Eq. (i), we get \[\frac{16}{9}{{y}^{2}}+{{y}^{2}}=100\] \[\Rightarrow \] \[{{y}^{2}}=\frac{100\times 9}{25}=36\] \[\Rightarrow \] \[y=6\text{ }m\]You need to login to perform this action.
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