If D, E and F are the mid-points of the sides | vedclass

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(D) Let the side length of the equilateral triangle $ABC$ be $2a$. Since $D, E,$ and $F$ are the mid-points of sides $BC, AB,$ and $AC$ respectively,t

Vedclass · Accepted Answer

$1:1$

Vedclass · Answer

(D) Let the side length of the equilateral triangle $ABC$ be $2a$. Since $D, E,$ and $F$ are the mid-points of sides $BC, AB,$ and $AC$ respectively,the lengths of the segments are $BD = DC = CE = EA = AF = FB = a$.By the Mid-point Theorem,the triangle $ABC$ is divided into four congruent equilateral triangles: $	riangle AEF, 	riangle EBD, 	riangle DFC,$ and $	riangle FED$,each with side length $a$.Since all four triangles are congruent,their areas are equal.Therefore,$	ext{Area}(	riangle DEF) = 	ext{Area}(	riangle DFC)$.The ratio of the area of $	riangle DEF$ to the area of $	riangle DFC$ is $1:1$.

If $D, E$ and $F$ are the mid-points of the sides of an equilateral triangle $ABC,$ then the ratio of the area of triangle $DEF$ and $DCF$ is

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