What is the length of a fence required to enclose a rectangular field of length 50 m and breadth 40 m?
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Answer:
Given,
dimensions of rectangular field =50m×40m
cost of flowering bed = 30Rs/m
2
cost of grovelling path = 20Rs/m
2
Ref. image
Let width of gravel =x m
area of field = 50×40=2000m
2
area of flower bed = (50−2x)(40−2x)
Total cost
= cost of flower bed+ grovelling path
∴52000=[(50−2x)(40−2x)×30] +[(2×50×x)+2(40−2x)x]×20
=52000=[(2000−100x−80x+4x
2
)×30] +[100x+80x−4x
2
]×20
=52000=60000−5400x+120x
2
+3600x−8x
2
=40x
2
−1800x+8000=0
=x
2
−45x+200=0
∴x=5,40
40 can't be the value of x as
it is the total field width
∴x=5m
Thus, gravel path width is 5m
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