Q2 of 62 Page 180

In the figure, AP = 3 cm, AR = 4.5 cm, AQ = 6 cm, AB = 5 cm, and AC = 10 cm. Find the length of AD.

Given: AP = 3 cm, AR = 4.5 cm, AQ = 6 cm, AB = 5 cm, and AC = 10 cm

Required: Find the length of AD


Consider the ΔABC


Here, PB = AB—AP = 5—3 = 2cm and QC = AC—AQ = 10—6 = 4cm


Now, and


Here, we can clearly see that


∴ By Converse Thales theorem PQ||BC (∵)


Now Consider Δ ABD


Here, PR|| BD


∴ BY Thales theorem


⇒


⇒


⇒


⇒ RD = 3cm


∴ AD = AR + RD = 4.5 + 3 = 7.5 cm


∴ Length of AD = 7.5cm


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