Question

In the figure ,PC ,Qk and BC ,Hk are parllel .If AQ= 6cm ,QH= 4cm ,HP= 5cm and KC = 18 cm ,then find the lengths of AK and AB .

Answer 1

Step-by-step explanation:

Given In the figure ,PC ,Qk and BC ,Hk are parallel .If AQ = 6 cm ,QH = 4 cm ,HP= 5 cm and KC = 18 cm ,then find the lengths of AK and PB

• Given PC is parallel to QK and BC is parallel to HK
• So AQ = 6 cm, QH = 4 cm, HP = 5 cm, KC = 18 cm
• We need to find length of AK and PB.
• Consider the triangle APC
• So PC is parallel to QK
• AQ / QP = AK / KC (By Thales theorem)
• Here QP = QH + HP
•                 = 4 + 5 = 9 cm
• Now 6/9 = AK / 18
• Therefore AK = 6 x 18 / 9
•                         = 12 cm
• Now consider triangle ABC
• Here BC is parallel to HK
• Therefore AH / HB = AK / KC (By Thales theorem)
• So AH = AQ + QH = 6 + 4 = 10 cm
• So 10 / HB = 12/18
• HB = 10 x 18 / 12
• HB = 15 cm
• PB = HB – HP
•         15 – 5
•      = 10 cm
• Therefore PB = 10 cm

So length of PB and AK are 10 cm and 12 cm respectively

Answer 2

Answer:

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