Question

A rhombus is inscribed in triangle ABC in such a way that one of its vertices is A and two its sides lie along AB and AC where AC $=6$, AB $=12$ and BC $=8$ the side of the rhombus is?

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is C $4$

Given that a rhombus is inscribed in $△ABC,$

$\Rightarrow AC=6,$ $AB=12$ and $BC=8$

Let $R$ be a vertex of the rhombus on the side B.

Then, since $PR$ is parallel to $AC,$ we see that $△BPR$ and $△BAC$ are similar. So we have $BP:BA=PR:AC$

$\therefore 12-S:12=S:6$

$\Rightarrow S=4.$

Hence, the answer is $4.$