In $\triangle ABC$ where $AB = AC$, $D$ and $E$ are points on $AB$ and $AC$ respectively, such that $AB = 4BD$ and $AC = 4AE$.

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In $\triangle ABC$ where $AB = AC$, $D$ and $E$ are points on $AB$ and $AC$ respectively, such that $AB = 4BD$ and $AC = 4AE$. If area of quadrilateral $BCED$ is $52$ $cm^2$ and $[\triangle ADE] = x$ $cm^2$, find $x$.

What I Tried: Here is a picture :-

The only thing I am not able to figure out is that how to use the area of the quadrilateral using the available information in the picture. Suppose I am able to find the value of $y$, but how will I use that to find $[\Delta ADE]$ too? I cannot find a way to do that either.

Can anyone help me? Thank You.

Best Answer

You can use

$$ \dfrac{[ADE]}{[ABC]} = \dfrac{\tfrac{1}{2}\cdot AD \cdot AE \cdot \sin A}{\tfrac{1}{2}\cdot AB \cdot AC \cdot \sin A} $$

to know their ratios. And you know their difference.

Best Answer

Related Solutions

Given a point $P$ outside equilateral $\Delta ABC$ but inside $\angle ABC$, if the distance between $P$ to $BC,CA,AB$ are $h_1,h_2,h_3$ respectively.

In $\triangle ABC, AB = 28, BC = 21$ and $CA = 14$. Points $D$ and $E$ are on $AB$ with $AD = 7$ and $\angle ACD = \angle BCE$

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