Question

In $\Delta ABC$ above, $AB=AC$, $E$ is the midpoint of$\overline{AB}$, and D is the midpoint of $\overline{AC}$. If $AE=x$ and $ED=4$, what is length $BC$?

• A. $6$
• B. $8$
• C. $2x$
• D. $4x$
• E. $4x^2$

Answer 1

The correct option is B $8$

Given triangle $AB=AC$ and $E$ is mid point of $AB$ and $D$ is the mid point of $AC$

Then $AB=2AE$ and $AC=2AC$

$\Delta AED\approx >ABC$

$\Rightarrow \frac{AE}{AB}=\frac{AD}{AC}=\frac{ED}{BC}$

$\Rightarrow \frac{AE}{AB}=\frac{ED}{BC}$

Let $AE=x$, then $AB=2x$ and given $ED=4$

Then $\frac{x}{2x}=\frac{4}{BC}$

$\Rightarrow \frac{1}{2}=\frac{4}{BC}$

$\Rightarrow BC=4\times 2=8$