Question

Find the area of the triangle made by the line $2x+3y=12$ with the co-ordinate axes.

Answer 1

The given equation of the line $2x+3y=12$ can be written as $\frac{x}{6}+\frac{y}{4}=1$.

From the equation it is clear that the line made intercepts of length $6$ and $4$ from the $x$ and $y$ axes respectively.

Then we get a triangle whose base is $6$ units and perpendicular is $4$ units.

Then area of the triangle is $\frac{1}{2}\times 6\times 4=12$ unit${}^2$.