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Step-3

Title: Angle bisector theorem

Grade: 7-a Lesson: S3-L1

Explanation:

Step	Type	Explanation	Answer
1	Problem	Find value of AC. $3$
2	Given	ABC is a traingle and AD is the anglular bisector of \$\angle A\$, and sides AB = 25, BD = 5, and DC = 2.
3	Step	From the given \$\triangle ABC\$, according to the angle bisector theorem, we have	\begin{align} && \frac{BD}{DC} &= \frac{AB}{AC} \\ \end{align}
4	Step	Substitute the values.	\begin{align} \Rightarrow && \frac{5}{2} &= \frac{25}{AC} \\ \end{align}
5	Step	Multiply.	\begin{align} \Rightarrow && 5AC &= 50 \\ \end{align}
6	Step	cancel out common factor.	\begin{align} \require{cancel} \Rightarrow && AC &= \frac{\cancel{50} ^{10}}{\cancel{5} ^1} \\ \end{align}
7	Step	Answer	The value of AC = 10.

Step

Type

Explanation

Answer

Problem

Find value of AC.

$3$

Given

ABC is a traingle and AD is the anglular bisector of \$\angle A\$,
and sides AB = 25, BD = 5, and DC = 2.

Step

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

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

Step

Substitute the values.

\begin{align} \Rightarrow && \frac{5}{2} &= \frac{25}{AC} \\ \end{align}

Step

Multiply.

\begin{align} \Rightarrow && 5AC &= 50 \\ \end{align}

Step

cancel out common factor.

\begin{align} \require{cancel} \Rightarrow && AC &= \frac{\cancel{50} ^{10}}{\cancel{5} ^1} \\ \end{align}

Step

Answer

The value of AC = 10.