Question

In the figure,PQ is parallel to MN. If KP / PM = 4 / 13 and KN = 20.4 cm, then find KQ.

Answer 1

Answer:

Step-by-step explanation:

PQ║ MN ∴ BY THALES THEOREM ,

KP / PM =  KQ / QN

⇒4 / 13 = KQ / KN - KQ

⇒4 / 13 = KQ / 20.4 - KQ

⇒4 × ( 20.4 - KQ ) = 13KQ

⇒(4 × 20.4) - 4KQ = 13KQ

⇒81.6 = 4KQ = 13KQ

⇒13KQ - 4KQ = 81.6

⇒17KQ = 81.6

⇒KQ = 4.8

∴ LENGTH OF KQ = 4.8 cm

Answer 2

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In Triangle KMN, We have

PQ // MN

Therefore, KP/PM = KQ/QN

KP/PM = KQ/KN-KQ

4/13 = KQ / 20.4 - KQ

4(20.4 - KQ ) = 13 KQ

81.6 - 4KQ = 13 KQ

17 KQ = 81.6

KQ = 81.6/17

⇒ 4.8 cm.

Hence, the value of KQ = 4.8 cm .

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