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Step-2

Title: Angle bisector theorem

Grade: 7-a Lesson: S3-L1

Explanation:

Step	Type	Explanation	Answer
1	Problem	Find value of m. $2$
2	Given	ABC is a traingle and AD is the anglular bisector of \$\angle A\$, and sides AB = 3, BD = 18, and AC = 4.
3	Step	From the given \$\triangle ABC\$, according to the angle bisector theorem, we have	\begin{align} \require{cancel} && \frac{AB}{AC} &= \frac{BD}{DC} \\ \end{align}
4	Step	Substitute the values.	\begin{align} \Rightarrow && \frac{3}{4} &= \frac{18}{m} \\ \end{align}
5	Step	Multiply.	\begin{align} \Rightarrow && 3m &= 72\\ \end{align}
6	Step	Cancel out common factor.	\begin{align} \require{cancel} \Rightarrow && \cancel{3} ^1m &=\cancel{72} ^{24} \\ \end{align}
7	Step	Answer	The value of m = 24.

Step

Type

Explanation

Answer

Problem

Find value of m.

$2$

Given

ABC is a traingle and AD is the anglular bisector of \$\angle A\$, and sides AB = 3, BD = 18, and AC = 4.

Step

From the given \$\triangle ABC\$, according to the angle bisector theorem, we have

\begin{align} \require{cancel} && \frac{AB}{AC} &= \frac{BD}{DC} \\ \end{align}

Step

Substitute the values.

\begin{align} \Rightarrow && \frac{3}{4} &= \frac{18}{m} \\ \end{align}

Step

Multiply.

\begin{align} \Rightarrow && 3m &= 72\\ \end{align}

Step

Cancel out common factor.

\begin{align} \require{cancel} \Rightarrow && \cancel{3} ^1m &=\cancel{72} ^{24} \\ \end{align}

Step

Answer

The value of m = 24.