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Byju's Answer
Standard XII
Mathematics
Perpendicular Distance of a Point from a Line
The area of t...
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
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Solution
(c) 24 sq units
Given:
x
+
3
y
=
12
or,
y
=
12
-
x
3
When
x
=
0
, then
y
=
12
3
=
4
When
x
=
3
, then
y
=
9
3
=
3
When
x
=
6
, then
y
=
6
3
=
2
When
x
=
9
, then
y
=
3
3
=
1
When
x
=
12
, then
y
=
0
3
=
0
Thus, we get the following table:
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
A
O
E
, such that
A
O
=
4
unit and
O
E
=
12
unit.
Therefore,
a
r
e
a
o
f
△
A
O
E
=
1
2
(
b
a
s
e
×
h
e
i
g
h
t
)
=
1
2
(
O
E
×
A
O
)
=
1
2
×
12
×
4
=
24
sq units
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Q.
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