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Triangles

If Δ ABC is a...

Question

If $Δ A B C$ is an equilateral triangle and D, E and F are the midpoints of their respective sides, find the ratio of area of $Δ A B C$ to that of $Δ A D E + Δ D B F + Δ E F C .$

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Solution

The correct option is B

Area of $Δ$ ADE= $\frac{1}{4}$ Area of $Δ$ ABC

Area of $Δ$ ADE = Area of $Δ$ DBF = Area of $Δ$ EFC

Area of $Δ$ ADE + Area of $Δ$ DBF + Area of $Δ$ EFC

= $\frac{3}{4}$ Area of $Δ$ ABC

$\Rightarrow \frac{A r e a o f Δ A B C}{A r e a o f Δ A D E + Δ A r e a o f Δ D B F + A r e a o f Δ E F C} = \frac{4}{3}$

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