Question

In the figure below $PQ\parallel AB$, $CQ=4.8$ cm, $QB=3.6$ cm and $AB=6.3$ cm. Find $PQ$.

• A. $3.6$ cm
• B. $4.6$ cm
• C. $5.6$ cm
• D. $3.9$ cm

Answer 1

The correct option is A $3.6$ cm

Since $PQ\parallel AB$, we have the triangles $ABC$ and $PQC$ congruent to each other, as the angles formed are the same.

Since the two triangles are congruent, the ratio of corresponding sides will be the same.

Thus $\frac{AB}{PQ}=\frac{BC}{QC}$

$\Rightarrow \frac{AB}{PQ}=\frac{BQ+QC}{QC}$

$\Rightarrow \frac{6.3}{PQ}=\frac{4.8+3.6}{4.8}$

$\Rightarrow PQ=3.6$ cm