Question

# The area of the triangle formed by the line x + 3y = 12 and the coordinate axes is (a) 12 sq units (b) 18 sq units (c) 24 sq units (d) 30 sq units

Open in App
Solution

## (c) 24 sq units Given: $x+3y=12$ or, $y=\frac{12-x}{3}$ When $x=0$, then $y=\frac{12}{3}=4$ When $x=3$, then $y=\frac{9}{3}=3$ When $x=6$, then $y=\frac{6}{3}=2$ When $x=9$, then $y=\frac{3}{3}=1$ When $x=12$, then $y=\frac{0}{3}=0$ Thus, we get the following table: $\text{x}$ 0 3 6 9 12 $y$ 4 3 2 1 0 Plot these points on the graph paper. Join them to get a right-angled triangle $AOE$, such that $AO=4$ unit and $OE=12$ unit. Therefore, $areaof△AOE=\frac{1}{2}\left(base×height\right)=\frac{1}{2}\left(OE×AO\right)=\frac{1}{2}×12×4=24$ sq units

Suggest Corrections
0
Related Videos
Line and a Point
MATHEMATICS
Watch in App