A) 1 : 3
B) \[\sqrt{3}:4\]
C) 1 : 2
D) 1 : 4
Correct Answer: C
Solution :
Here, \[A{{C}^{2}}=2A{{B}^{2}}\] |
As \[\Delta ABE\]and \[\Delta ABC\]are equiangular, |
So, \[\Delta ABE\sim \Delta ABC\] |
[The ratio of the areas of two similar triangle is equal to the ratio of their corresponding sides] |
\[\frac{\text{Area}\,\,\text{of}\,\,\Delta ABE}{\text{Area}\,\,\text{of}\,\,\Delta ACF}=\frac{A{{B}^{2}}}{A{{C}^{2}}}=\frac{A{{B}^{2}}}{2A{{B}^{2}}}=\frac{1}{2}\] |
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