question_answer

Inside a triangular garden, there is a flower bed in the form of a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the garden are double of the corresponding sides of the flower bed. The areas of the path and the flower bed are in the ratio

A)  1 : 1                      

B)  1 : 2

C)  1 : 3                   

D)         3 :1  

Correct Answer: D

Solution :

 \[\Delta \,ABC-\Delta \,DEF\]                 \[\frac{Area\,of\,\Delta \,ABC}{Area\,of\,\Delta \,DEF}=\frac{{{(BC)}^{2}}}{{{(EF)}^{2}}}=\frac{{{(2a)}^{2}}}{{{a}^{2}}}=\frac{4}{1}\]                 \[\frac{Area\,of\,\Delta \,ABC-Area\,of\,\Delta \,DEF}{Area\,of\,\Delta \,DEF}=\frac{4-1}{1}=\frac{3}{1}\] \[\therefore \]  Area of path : Area of flower bed \[=3:1\].