Question : In $\triangle$ABC the height CD intersects AB at D. The mid-points of AB and BC are P and Q, respectively. If AD = 8 cm and CD = 6 cm then the length of PQ is:
Option 1: 3 cm
Option 2: 7 cm
Option 3: 9 cm
Option 4: 5 cm
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Correct Answer: 5 cm
Solution : Given: AD = 8 cm and CD = 6 cm $\angle$CDA = 90° So, from Pythagoras theorem we get, AC 2 = AD 2 + CD 2 ⇒ AC = $\sqrt{8^2+6^2}$ ∴ AC = 10 cm The straight line joining the midpoints of two sides of a triangle is parallel to the third side and half of the third side. So, PQ = $\frac{1}{2}×$AC ⇒ PQ = $\frac{1}{2}×10$ ∴ PQ = 5 cm Hence, the correct answer is 5 cm.
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