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.

Answer 1

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.