IN the diagram, |LN| = 4cm, LNM = 90o and tan y = 2/3. What is the area of the ∆LMN?
A.
24cm2
B.
12cm2
C.
10cm2
D.
6cm2
Correct answer is B
\(tan \hspace{1mm}y = \frac{opp}{adj}=\frac{2}{3}\Rightarrow \frac{2}{3}=\frac{
LN}{MN}=\frac{4}{MN}\\
∴ MN = \frac{12}{2}=6\\
Area \hspace{1mm}of \hspace{1mm}\Delta LMN = \frac{1}{2}\times MN\times LN=\frac{1}{2}\times 6\times 4=12cm\)