ABC and BDE are two equilateral triangles suc | vedclass

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(B) We know that all equilateral triangles have all their angles equal to $60^{\circ}$ and all their sides of the same length. Therefore,all equilater

Vedclass · Accepted Answer

$4:1$

Vedclass · Answer

(B) We know that all equilateral triangles have all their angles equal to $60^{\circ}$ and all their sides of the same length. Therefore,all equilateral triangles are similar to each other.The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.Let the side length of $	riangle ABC$ be $x$.Since $D$ is the mid-point of $BC$,the side length of $	riangle BDE$ is $\frac{x}{2}$.Therefore,the ratio of the areas is:$\frac{	ext{Area}(	riangle ABC)}{	ext{Area}(	riangle BDE)} = \left(\frac{x}{\frac{x}{2}}ight)^{2} = (2)^{2} = \frac{4}{1}$.Hence,the ratio is $4:1$,and the correct answer is $(B)$.

$ABC$ and $BDE$ are two equilateral triangles such that $D$ is the mid-point of $BC$. The ratio of the areas of triangles $ABC$ and $BDE$ is

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