Question

In ∆ABC,PQ|| BC, if AP - 2.4cm, AQ=2cm
QC = 3cm and BC = 6Cm , AB and PQ are respectively.
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Answer 1

Answer:

Given: Δ ABC, AP = 2.4 cm, AQ = 2 cm, QC = 3 cm, and BC = 6 cm. Also, PQ ∥ BC. Required to find: AB and PQ. By using Thales Theorem, we have [As it’s given that PQ ∥ BC] APPB=AQQCAPPB=AQQC 2.4PB=232.4PB=23 2 x PB = 2.4 x 3 PB = (2.4×3)2(2.4×3)2 cm ⇒ PB = 3.6 cm Now finding, AB = AP + PB AB = 2.4 + 3.6 ⇒ AB = 6 cm Now, considering Δ APQ and Δ ABC We have, ∠A = ∠A ∠APQ = ∠ABC (Corresponding angles are equal, PQ||BC and AB being a transversal) Thus, Δ APQ and Δ ABC are similar to each other by AA criteria. Now, we know that Corresponding parts of similar triangles are propositional. ⇒ APABAPAB = PQBCPQBC ⇒ PQ = (APABAPAB) x BC = (2.462.46) x 6 = 2.4 ∴ PQ = 2.4 cm