Question

in the given figure ABC is equilateral triangle . DE is parallel to BC such that area of quadrilateral DBCE is equal one half the area of triangle ABC. If BC=2cm then DE?​

Answer 1

Answer:

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Answer 2

Given:

in the given figure ABC is equilateral triangle . DE is parallel to BC such that area of quadrilateral DBCE is equal one half the area of triangle ABC. If BC=2cm then DE?

Solution:

Refer the image given below,

Know that, the ratio of the areas of two similar triangle is equal to the ratio of the squares of their corresponding sides.

In a equilateral triangle ABC, $\[DE\parallel BC\]$.

Therefore,

$\[\Delta ABC \sim \Delta ADE\]$

Given that the area of quadrilateral DBCE is equal one half the area of triangle ABC.

Therefore,  the area of quadrilateral DBCE is equal to area of the triangle ADE. that is one half the area of triangle ABC.

Take $\[\Delta ABC\,{\rm{and}}\,\Delta ADE\]$

$\[ \Rightarrow \frac{{Ar\,\Delta ABC}}{{Ar\,\Delta ADE}} = \frac{{B{C^2}}}{{D{E^2}}}\]$

$\[ \Rightarrow \frac{2}{1} = \frac{{{2^2}}}{{D{E^2}}}\]$

$\[\begin{array}{l} \Rightarrow D{E^2} = 2\\ \Rightarrow DE = \sqrt 2 \end{array}\]$

Hence, the length of DE is $\[\sqrt 2 \]$ cm.