Answer:
40 sq units
Step-by-step explanation:
[tex]5x + 10y = 8\\\Rightarrow y=\dfrac{8-5x}{10}\\\Rightarrow y=-\dfrac{1}{2}x+\dfrac{2}{5}[/tex]
Slope of [tex]L_2[/tex] is [tex]m_2[/tex]
[tex]m_1m_2=-1\\\Rightarrow m_2=-\dfrac{1}{m_1}\\\Rightarrow m_2=-\dfrac{1}{-\dfrac{1}{2}}\\\Rightarrow m_2=2[/tex]
[tex]L_2[/tex] passes through point [tex](8,6)[/tex]
[tex]y-6=2(x-8)\\\Rightarrow y=2x-16+6\\\Rightarrow y=2x-10[/tex]
Point at x axis where [tex]L_2[/tex] intersects is
[tex]0=2x-10\\\Rightarrow x=\dfrac{10}{2}\\\Rightarrow x=5[/tex]
Point [tex]A[/tex] of the triangle will be [tex](5,0)[/tex]
[tex]L_2[/tex] intersects line [tex]x=-3[/tex]. The point is
[tex]y=2\times(-3)-10\\\Rightarrow y=-6-10\\\Rightarrow y=-16[/tex]
The points of the triangle are [tex]A(5,0), O(0,0), B(-3,-16)[/tex]
Area of triangle is given by
[tex]A=\dfrac{|A_x(B_y-O_y)+B_x(A_y-O_y)+O_x(A_y-B_y)|}{2}\\\Rightarrow A=\dfrac{|5(-16-0)+-3(0-0)+0(0-(-16))|}{2}\\\Rightarrow A=40\ \text{sq units}[/tex]
The area of the triangle is 40 sq units.
