178k views
4 votes
Triangles FIM and LAK below are similar with m

Triangles FIM and LAK below are similar with m-example-1

1 Answer

3 votes

8

Step-by-step explanation

as the triangles are similar we can set a proportion

Step 1

Let


\text{ratio}=\frac{\text{longest side}}{\text{smallest side}}

so

a) for triangle FIM


\begin{gathered} \text{ratio}=\frac{\text{longest side}}{\text{middle side}} \\ ratio_1=(FM)/(FI)=(6)/(4)=(3)/(2) \\ ratio_1=(3)/(2) \end{gathered}

b) for triangle LAK


\begin{gathered} \text{ratio}=\frac{\text{longest side}}{\text{smallest side}} \\ ratio_2=(LK)/(LA)=(12)/(LA) \\ ratio_2=(12)/(LA) \end{gathered}

as the tringles are similar, the ratios are similar

hence


\begin{gathered} \text{ratio}_1=ratio_2 \\ (3)/(2)=(12)/(LA) \end{gathered}

Step 2

now, solve for LA


\begin{gathered} (3)/(2)=(12)/(LA) \\ \text{cross multiply } \\ 3\cdot LA=12\cdot2 \\ 3LA=24 \\ \text{divide both sides by 3} \\ (3LA)/(3)=(24)/(3) \\ LA=8 \end{gathered}

therefore, the answer i

8

I hope this helps you

User GideonKain
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories