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, AC2 = AD2 + CD2 ⇒ 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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Question : The mid-points of AB and AC of the $\triangle$ABC are P and Q, respectively. If PQ = 6 cm, then the side BC is:
Option 1: 10 cm
Option 2: 12 cm
Option 3: 8 cm
Option 4: 14 cm
Question : In $\triangle$ABC, two medians BE and CF intersect at the point O. P and Q are the midpoints of BO and CO, respectively. If the length of PQ = 3 cm, then the length of FE will be:
Option 2: 6 cm
Option 4: 12 cm
Question : $\triangle ABC$ is a triangle. PQ is a line segment intersecting AB in P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and the length of PQ is 18 cm. The length of BC is:
Option 1: 28 cm
Option 2: 48 cm
Option 3: 84 cm
Option 4: 42 cm
Question : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.
Option 1: 18 cm
Option 2: 16 cm
Option 3: 20 cm
Option 4: 22 cm
Question : In $\triangle$ABC, $\angle$A = 90°, AD$\perp$BC and AD = BD = 2 cm. The length of CD is:
Option 2: 3.5 cm
Option 3: 3.2 cm
Option 4: 2 cm
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