Q40 / 110 · VITEEE 2024 · Mathematics

In a triangle $A B C$ as shown in the diagram, where $A B=5, A C=10$ and $B D=1$, then perimeter of $\triangle A B C$ is

A
9
Correct answer
B
18
C
20
D
30

Solution

$\because A D$ divides $\angle B A C$ is two equal parts. So, by angle bisector formula $\begin{aligned} & \frac{B D}{D C}=\frac{A B}{A C} \Rightarrow \frac{1}{D C}=\frac{5}{10} \\ \Rightarrow \quad & D C=2 \end{aligned}$ Therefore, $B C=B D+D C=1+2=3$ Hence, perimeter of $\triangle A B C=A B+B C+C A$ $=5+3+10=18$

Hence, the correct answer is option: 'B'.

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