Consider the lines $y=3 x, y=6 x$ and $y=9$ What is the area of the triangle formed by these lines?

• Correct answer
  A

  $\frac{27}{4}$ square units
• B

  $\frac{27}{2}$ square units
• C

  $\frac{19}{4}$ square units
• D

  $\frac{19}{2}$ square units

Solution

$O A B$ is triangle.
$\begin{aligned} \text { Area of triangle } & =\frac{1}{2} \times \text { base } \times \text { height }=\frac{1}{2} \times \mathrm{AB} \times \mathrm{OP} \\ & =\frac{1}{2} \times \frac{3}{2} \times 9=\frac{27}{4} \end{aligned}$ Area of triangle $=\frac{27}{4}$ square units

Hence, the correct answer is option: 'A'.