Question

a rectangular garden of length 50 m and breadth 40 m and wide 5m find the area of path find the cost of constructing it at the rate of 40 per m²​

Answer 1

Answer:

The dimensions of a rectangular field are 50 m by 40 m. A flower bed is prepared inside this field leaving a gravel path of uniform width all round the flower bed. The total cost of laying the flower bed and gravelling the path at Rs 30 and Rs 20 per square metre, respectively is Rs 52,000. Find the width of the gravel path.

Step-by-step explanation:

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

Answer 2

Given :-

→ Length of rectangular garden = 50m

→ Breadth of rectangular garden = 40m

_____________________________

To Find :-

→ Area of rectangular field with 50m length and 40m breadth.

→ Cost of constructing the field at the rate of Rs.40 per sq. m.

_____________________________

Solution :-

Formula to find the area of rectangular field

$= L$ × $B$

Cost of constructing the rectangular field

$= Area$  × Cost of constructing per sq. m

_____________________________

Required Answer :-

Area of rectangular field

= L × B

= 50m × 40m

= 2000 sq. m

Cost of constructing the rectangular field

= Area × Cost of constructing the rectangular field

= 2000 sq. m × Rs.40

= Rs.80000

_____________________________