A rectangular field is 16 m long and 12 m wide . Inside the field there is path of 1•5 m wide all around . Find the area of remaining field.
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Let width of path x
Length =20+2x
Width =14+2x
Area of outer rectangular =l×b
=(20+2x)(14+2x)
=4x
2
+68x+280
Area of path:
4x
2
+68x+280−280=111
4x
2
+68x=111
4x
2
+68x−111=0
(4x
2
+74x−6x−111)=0
(2x−3)(2x+37)=0
x=
2
3
m or x=−
2
37
Since, width can not be −ve
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