A rectangular field is 36 m long and 30 m wide. A path of uniform width and area 360 m2 run around inside it. Find the width
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Answered by
1
Area of the rectangular feild
=
(
30
×
36
)
s
q
c
m
=
1080
s
q
m
Area of footpath+area of rectangle
=
360
+
1080
=
1440
s
q
m
Let the width of footpath be
x
m
Therefore,
Area of footpath
=
(
30
+
2
x
)
(
24
+
2
x
)
Therefore,
(
30
+
2
x
)
(
24
+
2
x
)
=
1080
=>
720
+
48
x
+
60
x
+
4
x
2
=
1080
=>
x
2
+
27
x
−
90
=
0
=>
x
2
+
30
x
−
3
x
−
90
=
0
=>
x
(
x
+
30
)
−
3
(
x
+
30
)
=
0
=>
(
x
+
30
)
(
x
−
3
)
=
0
x
=
−
30
or,
x
=
3
x
=
−
30
is not possible
Therefore,
x
=
3
Therefore, width
=
3
m
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