Home » » IN the diagram, |LN| = 4cm, LNM = 90o and tan y = 2/3. What is the area of the âˆ...

# IN the diagram, |LN| = 4cm, LNM = 90o and tan y = 2/3. What is the area of the âˆ...

### Question

IN the diagram, |LN| = 4cm, LNM = 90o and tan y = 2/3. What is the area of the âˆ†LMN?

### Options

A) 24cm2

B) 12cm2

C) 10cm2

D) 6cm2

$$tan \hspace{1mm}y = \frac{opp}{adj}=\frac{2}{3}\Rightarrow \frac{2}{3}=\frac{ LN}{MN}=\frac{4}{MN}\\∴ MN = \frac{12}{2}=6\\Area \hspace{1mm}of \hspace{1mm}\Delta LMN = \frac{1}{2}\times MN\times LN=\frac{1}{2}\times 6\times 4=12cm$$
• $$tan \hspace{1mm}y = \frac{opp}{adj}=\frac{2}{3}\Rightarrow \frac{2}{3}=\frac{ LN}{MN}=\frac{4}{MN}\\∴ MN = \frac{12}{2}=6\\Area \hspace{1mm}of \hspace{1mm}\Delta LMN = \frac{1}{2}\times MN\times LN=\frac{1}{2}\times 6\times 4=12cm$$