Question

If ∆ABC and ∆DEF are two triangles such tha\[\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{2}{5}\] , then Area (∆ABC) : Area (∆DEF) =

Options

• 2:5

• 4 : 25

• 4 : 15

• 8 : 125

Answer 1

Given: ΔABC and ΔDEF are two triangles such that `(AB)/(DE)=(BC)/(EF)=(CA)/(FD)=2/5`

To find: `\text{Ar(Δ ABC): Ar(Δ DEF)}`

We know that if the sides of two triangles are proportional, then the two triangles are similar.

Since `(AB)/(DE)=(BC)/(EF)=(CA)/(FD)=2/5`, therefore, ΔABC and ΔDEF are similar.

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

`\text{Ar(Δ ABC)}/\text{Ar(Δ DEF)}=(AB)^2/(DE)^2`

`\text{Ar(Δ ABC)}/\text{Ar(Δ DEF)}=2^2/5^2`

`\text{Ar(Δ ABC)}/\text{Ar(Δ DEF)}=4/25`

Hence the correct answer is `b`