In the given figure, AQ = 4√2 cm, QC = 6√2 cm and AB = 20 cm. If PQ is parallel to BC, then what is the value (in cm) of PB?

In the given figure, AQ = 4√2 cm, QC = 6√2 cm and AB = 20 cm. If PQ is parallel to BC, then what is the value (in cm) of PB?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \text{In }\Delta APQ\&\Delta ABC\\ & \frac{AP}{AB}=\frac{AQ}{AC}\\ & \frac{AP}{20}=\frac{4\sqrt{2}}{10\sqrt{2}}\\ & AP=\frac{20\times 2}{5}=8\text{ cm}\\ & PB=AB-AP=20-8=12\text{ cm}\end{array}$$