Question

in the figure, PC || QK and BC || HK, if AQ=6cm, QH=4cm, HP=5cm and KC=18cm, then find the lengths of AK and AB

Answer 1

Answer:

Step-by-step explanation:

Consider the ΔAPC

Here, PC||QK

∴ By Thales theorem  

Here, QP = QH + HP = 4 + 5 = 9cm  

∴ AK = 12cm

Now, Consider ΔABC

Here, BC||HK

∴  By Thales theorem

Here, AH = AQ + QH = 6 + 4 = 10cm

HB = 15cm

PB = HB—HP = 15—5 = 10cm

PB = 10cm

∴ Length of AK and PB are 12 cm and 10 cm respectively.

Answer 2

Given :

PC || QK And BC || HK , AQ = 6cm , QH = 4cm , HP = 5cm , KC =18cm :

Required :

Length Of AK And PB

Consider The ∆APC

Here, PC || QK

Therefore , By Thalas Theorem AQ = AK

QP = KC

Here, QP = QH + HP = 4 + 5 = 9cm

=> 6/9 = AE / 18

=> AK = 6 × 18 / 9 = 12

Therefore AK = 12cm

Now , Consider ∆ABC

Here , BC || HK

Therefore By Thalas Theorem AH = AK

HB = KC

Here , AH = AQ + QH = 6 + 4 = 10cm

=> 10 / HB = 12 / 18

=> HB = 10 × 18 / 12 = 15

=> HB = 15cm

=> PB = HB - HP = 15 - 5 = 10cm

Therefore , PB = 10cm

Therefore , Length Of AK And PB Are 12cm And 10cm Respectively...

Hope It Helps u

^_^