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

Answer 1

(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,
$areaof△AOE=\frac{1}{2}(base\times height)=\frac{1}{2}(OE\times AO)=\frac{1}{2}\times 12\times 4=24$ sq units