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
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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