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Byju's Answer
Standard IX
Mathematics
Evaluating Area When Side Is a Variable
A square lawn...
Question
A square lawn is surrounded by a path
2
m wide. If the area of the path is
240
m
2
. Find the area of the lawn.
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Solution
Let the side of lawn be 'a' m.
Area of lawn =
a
2
Length of outer side
=
(
a
+
4
)
m
Area of outer square
=
(
a
+
4
)
2
=
a
2
+
8
a
+
16
Area of the path = Area of outer sqare-Area of low
⇒
240
=
a
2
+
8
a
+
16
−
a
2
⇒
240
=
8
a
+
16
⇒
8
(
a
+
2
)
=
240
⇒
a
+
2
=
240
8
⇒
a
+
2
=
30
⇒
a
=
30
−
2
⇒
a
=
28
side of lawn
=
30
m
Area of lawn =
28
×
28
=
784
m
2
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Q.
A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m
2
, find the area of the lawn.