What will the ratio AB:AC be if C divides the line segment AB in the ratio 5:12?

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Question

What will the ratio $A B : A C$ be if $C$ divides the line segment $A B$ in the ratio $5 : 12$ ?

Options:

A .

5 : 12

B .

17 : 12

C .

12 : 17

D .

17 : 5

Answer: Option D
:
D

Given $\frac{A C}{B C} = \frac{5}{12}$

Therefore, $\frac{B C}{A C} = \frac{12}{5}$

$\frac{A B}{A C} = \frac{A C + B C}{A C} = 1 + \frac{B C}{A C} = 1 + \frac{12}{5} = \frac{17}{5}$

So, the required ratio $= 17 : 5$

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