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
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Correct Answer: 48 cm
Solution :
Given: AP : BP = 3 : 5
And PQ = 18 cm
Let BC = $x$ cm
In $\triangle$APQ and $\triangle$ABC,
$\frac{AP}{AB}=\frac{PQ}{BC}$ (since PQ is parallel to base BC)
Putting the values, we get:
$\frac{3}{8}=\frac{18}{x}$
$\therefore x=\frac{18×8}{3}$ = 48
Hence, the correct answer is 48 cm.
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