A) 2:1
B) 1:2
C) 4:1
D) 1:4
Correct Answer: C
Solution :
[c]: Given, ABC and BDE are two equilateral triangles. |
\[\Rightarrow \,\,\Delta ABC\]and \[\Delta BDE\] are equiangular. |
\[\therefore \,\,\,\Delta ABC\tilde{\ }\Delta BDE\] |
Since, ratio of areas of two similar triangles is equal to the square of the ratio of any two corresponding sides. |
\[\therefore \,\,\frac{ar(ABC)}{ar(\Delta BDE)}={{\left( \frac{AB}{BD} \right)}^{2}}={{\left( \frac{BC}{BD} \right)}^{2}}={{\left( \frac{2BD}{BD} \right)}^{2}}\] |
( Given, D is mid-point of BC \[\therefore \,BC=2BD\]) |
\[\Rightarrow \,\,\,\,\,\frac{ar\,(\Delta ABC)}{ar(\Delta BDE)}=\frac{4}{1}\] |
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