Question

In $\Delta ABC$ above, the length of $AB$ is $3$ and $D$ is the midpoint of $AC$. What is the length of $BC$?

• A. $3\sqrt{3}$ (approximately $5.20$)
• B. $4\sqrt{3}$ (approximately $5.66$)
• C. $4\sqrt{3}$ (approximately $6.93$)
• D. $5\sqrt{3}$ (approximately $8.49$)
• E. $5\sqrt{3}$ (approximately $8.66$)

Answer 1

The correct option is A $3\sqrt{3}$ (approximately $5.20$)

Triangle $ABD$ is equilateral triangle, so all sides are equal to $3$.

Also given that $D$ is midpoint of $AC$. Therefore $AD=AB=BD=DC=3$.

Now consider triangle $BDC$, $BD=CD=3$ and angle $BDC=120$.

So by applying cosine rule, we get $BC=3\sqrt{3}$.