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 side 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 :

Foundation

Mathematics Foundation

Similarity of Triangles

Area of Triangle

area of triangle and properties

Question

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 side 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 :

1 : 3

1 : 1

1 : 2

3 : 1

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$\frac{area of ΔABC}{area of ΔDEF} = \frac{{BC}^{2}}{{EF}^{2}}$
$\frac{area of ΔABC}{area of ΔDEF} = \frac{4}{1}$
   area of ΔABC = 4 area of ΔDEF
   Then the area of path = 3 area of DDEF
   Hence,
$\frac{area of the path}{area of flower bed} = \frac{3}{1}$