A) \[\text{10 cm}\]
B) \[\text{2}\sqrt{40}\text{ cm}\]
C) \[\sqrt{13}\text{ cm}\]
D) \[2\sqrt{13}\text{ cm}\]
Correct Answer: D
Solution :
[d] |
In right angled\[\Delta ABC,\] |
\[A{{D}^{2}}+C{{E}^{2}}=A{{B}^{2}}+B{{D}^{2}}+B{{C}^{2}}+B{{E}^{2}}\] |
\[=A{{B}^{2}}+\frac{1}{4}B{{C}^{2}}+B{{C}^{2}}+\frac{1}{4}A{{B}^{2}}\] |
\[\Rightarrow \,\,\,\,\,\,4(A{{D}^{2}}+C{{E}^{2}})=5(A{{B}^{2}}+B{{C}^{2}})\] |
\[\Rightarrow \,\,\,\,\,\,4(25+40)=5{{(AC)}^{2}}\] |
\[\Rightarrow \,\,\,\,\,\,A{{C}^{2}}=\frac{4\times 65}{5}\] |
\[\Rightarrow \,\,\,\,\,\,AC=2\sqrt{13}cm.\] |
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