Answer:
[tex]\dfrac{288}{17}\ un^2.[/tex]
Step-by-step explanation:
1. The line y=12-4x has the slope -4, then perpendicular line will have slope [tex]\dfrac{1}{4}.[/tex]
The equation of this perpendicular line is
[tex]y-0=\dfrac{1}{4}(x-0),\\ \\4y=x.[/tex]
2. The vertices of the triangle are at points:
A: x=0, y=0.
B: x=0, y=12.
C: [tex]\left\{\begin{array}{l}y=12-4x\\4y=x\end{array}\right.\Rightarrow y=12-16y,\ y=\dfrac{12}{17},\ x=\dfrac{48}{17}.[/tex]
3. The height of the triangle ABC is x-coordinate of point C, so [tex]h=\dfrac{48}{17},[/tex] the base of the triangle is the length of the segment AB, 12 cm.
4. The area of the triangle ABC is [tex]\dfrac{1}{2}\cdot 12\cdot \dfrac{48}{17}=\dfrac{288}{17}\ un^2.[/tex]
