Question

Triangles FIM and LAK below are similar with m

Answer 1

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