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Question
In a right-angled triangle ABC, ∠B = 90°, P and Q are the points on the sides AB and AC such as PQBC, AB = 8 cm, AQ = 6 cm and PA:AB = 1:3. Find the lengths of AC and BC.
Solution
In right-angled ΔABC,
PQ || BC
⇒ `"PA"/"AB" = "QA"/"AC"`
⇒ `(1)/(3) = (6)/"AC"`
⇒ AC = 18cm
By Pythagoras Theorem,
BC2 = AC2 - AB2
⇒ BC2 = 182 - 82
⇒ BC2 = 324 - 64
⇒ BC = 16.12cm.
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