The point C divides the line segment AB in the ratio 3:7. Find the length of AB (in cm) if the line segment BC is 3.5 cm long.

4 cm

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5 cm

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6 cm

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7 cm

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Solution

The correct option is B 5 cm
$\frac{A C}{B C} = \frac{3}{7}$
Therefore,
$\frac{A B}{B C} = \frac{B C}{B C} + \frac{A C}{B C} = 1 + \frac{3}{7} = \frac{10}{7}$
$\frac{A B}{B C} = \frac{10}{7}$
Now,
$A B = B C \times \frac{10}{7} = 3.5 \times \frac{10}{7} = 5 c m$

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