In fig- PQ is parallel to MN- If KP-PM - 4-13 and KN - 20-4 cm- Find KQ

In Δ KMN, we have PQ ∥ MN ∴KP/PM = KQ/QN nbsp; nbsp; [Basic proportionality Theorem] ⇒KP/PM = KQ/KN KQ ⇒4/13 = KQ/20.4 KQ ⇒ nbsp; 4(20.4 KQ) = 13 K ...

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Standard IX

Mathematics

Properties of Similar Triangles

In fig., PQ i...

Question

In fig., PQ is parallel to MN. If $\frac{K P}{P M} = \frac{4}{13}$ and KN = 20.4 cm. Find KQ

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Solution

In $Δ K M N$ , we have
$P Q ∥ M N$
$∴ \frac{K P}{P M} = \frac{K Q}{Q N}$ [Basic proportionality Theorem]
$\Rightarrow \frac{K P}{P M} = \frac{K Q}{K N - K Q}$
$\Rightarrow \frac{4}{13} = \frac{K Q}{20.4 - K Q}$
$\Rightarrow 4 (20.4 - K Q) = 13 K Q$
$\Rightarrow 81.6 - 4 K Q = 13 K Q$
$\Rightarrow 17 K Q = 81.6$
$\Rightarrow K Q = \frac{81.6}{17} = 4.8 c m$

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In fig., PQ is parallel to MN. If KPPM=413 and KN = 20.4 cm. Find KQ

In ΔKMN, we have PQ∥MN ∴KPPM=KQQN [Basic proportionality Theorem] ⇒KPPM=KQKN−KQ ⇒413=KQ20.4−KQ ⇒4(20.4−KQ)=13 KQ ⇒81.6−4 KQ=13 KQ ⇒17 KQ=81.6 ⇒KQ=81.617=4.8 cm

In fig., PQ is parallel to MN. If $\frac{K P}{P M} = \frac{4}{13}$ and KN = 20.4 cm. Find KQ