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Byju's Answer
Standard XII
Mathematics
Combination Based on Geometry
Two sides of ...
Question
Two sides of a square lie on the lines
x
+
y
=
1
and
x
+
y
+
2
=
0
What is the area?
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Solution
Clearly the length of the side of the square is equal to the distance between the parallel lines
x
+
y
−
1
=
0
....(i) and
x
+
y
+
2
=
0
.....(ii)
Putting
x
=
0
in (i) we get
y
=
1
So
(
0
,
1
)
is a point on line
(
i
)
Now Distance between the parallel lines
=
length of the
⊥
from
(
0
,
1
)
to
x
+
y
+
2
=
0
=
|
0
+
1
+
2
|
√
1
2
+
1
2
=
3
√
2
Thus the length of the side of the square is
3
√
2
and hence its area =
(
3
√
2
)
2
=
9
2
u
n
i
t
s
2
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