In $Δ A B C$ is an equilateral triangle, then the ratio of the area of the triangle in the area of its pedal triangle.

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$4 : 1$

$1 : 2$

$2 : 3$

$5 : 4$

answer is C.

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Detailed Solution

$Δ A B C$ is an equilateral triangle of side $' x'$

$\begin{array}{l} ∴ D E = E F = F D = x \cos 60 ° \\ = \frac{x}{2} \\ ∴ [Δ A B C] : [Δ D E F] = \frac{\sqrt{3}}{4} x^{2} : \frac{\sqrt{3}}{4} \frac{x^{2}}{4} \\ = 4 : 1 \end{array}$

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