Question

Inside a triangular garden, there is a flower bedding 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. $3:1$

Answer 1

Answer: (D)

$3:1$

$\Delta ABC\sim \Delta DEF$ ....given

$\frac{Areaof\Delta ABC}{Areaof\Delta DEF}=\frac{(BC{)}^2}{(EF{)}^2}=\frac{(2a{)}^2}{a^2}=\frac{4}{1}$

(since for similar triangles, ratio of area is square of ratio of sides)

$\Rightarrow \frac{Areaof\Delta ABC-Areaof\Delta DEF}{Areaof\Delta DEF}=\frac{4-1}{1}=\frac{3}{1}$ ....(by dividendo)

$\therefore \text{Area of path : Area of flower bed}=3:1$.