Question

Through a rectangular field of length 90m and breadth 60m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3m, Find:

(i) the area covered by the roads
(ii) the cost of constructing the roads at the rate of ₹110 per m²​

Answer 1

R.E.F. Image.

Given length of field = 90 m

width of field = 60 m.

Area of field =90×60

Area =5400m

2

length of road GEFH = 90 m.

length of road ABCD = 60 m.

width of each road = 3m [Given].

Area of roads =ar(ABCD)+ar.(GEFH)−ar(LIJK)

=90×3+60×3−3×3

=270+180−9

Area of roads =441m

2

.

∴ Area covered by roads =441m

2

.

cost of construction of roads =441×10

Total cost =4410Rs.

Answer 2

✲Question:-

• Through a rectangular field of length 90m and breadth 60m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3m, Find:

• (i) the area covered by the roads
• (ii) the cost of constructing the roads at the rate of ₹110 per m²

❖Given:-

• Length of rectangle = 90m
• Breadth of rectangle = 60 m
• Wodth of each road is 3m

❅To find:-

1. the area covered by the roads
2. the cost of constructing the roads at the rate of ₹110 per m²

✹Solution:-

$\sf \: ↦Area \: of \: roads = Area \: of \: EFGH+ \: Area \: of \: IJKL-Area \: of \: PQRS$

EFGH is a rectangle with

• EFGH is a rectangle withLength =3m
• EFGH is a rectangle withLength =3mBreadth = 60m

EFGH is a rectangle withLength =3mBreadth = 60m↦Area of EFGH= length ×breadth

↦3m×60m

↦180m

Area of EFGH is 180m²

IJKL is a rectangle with

• Length =90m
• Breadth =3m

Area of IJKL=length ×breadth

↠90m×3m

↠270m

Area of IJKL is 270 m²

PQRS is a square with

• side= 3m

Area of PQRS =side²

↠3m×3m

↠9m²

Area of PQRS is 9m²

↦Area of roads = Area of EFGH+ Area of IJKL-Area of PQRS

$↠180 + 270 - 9$

$↠450 - 9$

$↠441 {m}^{2}$

$\therefore \: Area \: covered \: by \: \: roads = 441 {m}^{2}$

2)the cost of constructing the roads at the rate of ₹110 per m

=> Cost of constructing 1m² road = Rs.110

$\sf \: so \: cost \: of \: constructing \:441 {m }^{2} \: road = ₹110×441$

$\implies \: ₹48,510$

∴The cost of constructing the road is Rs.48510

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