In ∆ ABC, the height CD intersects AB at D. The mid-points

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In ∆ 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

1. 3 cm
2. 7 cm
3. 9 cm
4. 5 cm

Correct Option: D

On the basis of question we draw a figure of triangle ABC ,

From ∆ ACD,
Given , AD = 8 cm.
CD = 6 cm.
∠CDA = 90°
∴ AC = √AD² + DC²
AC = √8² + 6²
AC = √64 + 36
AC = √100 = 10 cm
The straight line joining the midpoints of two sides of a triangle is parallel to the third side and half of third side.

∴ PQ =	1	AC =	10	= 5cm.
	2		2