Question

In the given figure, PQ is parallel to MN. If $\frac{KP}{PM}=\frac{4}{13}$ and KN = 20.4 cm. Find KQ.

• A. 6 cm
• B. 5.6 cm
• C. 4.8 cm
• D. 9.2 cm

Answer 1

The correct option is C

4.8 cm

In $\Delta KMN$, we have

$PQ\parallel MN$

$\therefore \frac{KP}{PM}=\frac{KQ}{QN}$ [Basic proportionality Theorem]

$\Rightarrow \frac{KP}{PM}=\frac{KQ}{KN-KQ}$

$\Rightarrow \frac{4}{13}=\frac{KQ}{20.4-KQ}$

$\Rightarrow 4(20.4-KQ)=13KQ$

$\Rightarrow 81.6-4KQ=13KQ$

$\Rightarrow 17KQ=81.6$

$\Rightarrow KQ=\frac{81.6}{17}=4.8cm$