Question

The area of the triangle formed by the line $x+3y=12$ and the coordinate axes is:

• A. $12sq.units$
• B. $18sq.units$
• C. $24sq.units$
• D. $30sq.units$

Answer 1

The correct option is C

$24sq.units$

Explanation for the correct option:

Step 1: Finding the points at which the line cuts the $x$-axis and $y$-axis

The equation of the line is $x+3y=12$

The point at which the line cuts $x$-axis will have its $y$- coordinate $0$.

Substituting $y=0$ in the equation we get,

$$\begin{gathered} x+3y=12 \\ \Rightarrow x+3\left(0\right)=12 \\ \Rightarrow x=12 \end{gathered}$$

The point is $(12,0)$

The point at which the line cuts $y$-axis will have its $x$-coordinate $0$.

Substituting $x=0$ in the equation we get,

$$\begin{gathered} x+3y=12 \\ \Rightarrow 3y=12 \\ \Rightarrow y=4 \end{gathered}$$

The point on $y$-axis is $(0,4)$

Step 2: Finding the area of the triangle

The triangle will be a right-angled triangle as it will cut through both axes.

Area of the triangle $=$$\frac{1}{2}$$\times$base of the triangle $\times$height of the triangle

$$\begin{gathered} =\frac{1}{2}\times 4\times 12 \\ =24sq.units \end{gathered}$$

Hence, the correct answer is option C.