Question

A lawn 50 m long and 40 m broad has a path 8 m broad outside it. find the area path and the cost of levelling it @rupees. 50 per square metre. ​

Answer 1

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