Find out the area of a square field whose sides are 47m long after making a 5m long road in the north and west direction.
Answers
Let the width of the gravel path be x metres. Then, Each side of the square flower bed is (44−2x) metres
Now, Area of the square field 44×44=1936m
2
Area of the flower bed =(44−2x)
2
m
2
Area of the gravel path= Area of the field - Area of the flower bed
=1936−(44−2x)
2
=1936−(1936−176x+4x
2
)=(176−4x
2
)m
2
Cost of laying the flower bed=Area of the flower bed × Rate per sq.m
=(44−2x)
2
×
100
275
=
4
11
(44−2x)
2
=11(22−x)
2
Cost of gravelling the path = Area of the path × Rate per sq. m
=(176x−4x
2
)
100
150
=6(44−x
2
)
It is given that the total cost of laying the flower bed and gravelling the path is Rs. 4904
∴11(22−x)
2
+6(44x−x
2
)=4904
⇒5x
2
−220x+5324=4908
⇒5x
2
−220x+420=0⇒x
2
−44x+84=0⇒x
2
−42x−2x+84=0
⇒(x−2)(x−42)=0⇒x=2orx=42
But x
=42 as the side of the square is 44m. therefore, x=2
Hence the width of the gravel path is 2 metres