Question

Two cross road each of with 10 m, cut at right angle through the centre of a rectangular park of length 500 m and 300 m and parallel to its side. Find the area of road also. Find the cost of constructing the roads at the rate of rupees 70 per square metre​

Answer 1

Answer:

Here, PQ=10m and PS=300m, EH=10m and EF=700m

And KL=10m and KN=10m

Area of roads = Area of PQRS+Area of EFGH−Area of KLMN

[∵ KLMN is taken twice, which is to be subtracted]

=PS×PQ+EF×EH−KL×KN

=(300×10)+(700×10)−(10×10)

=3000+7000−100

=9,900m

2

Area of road in hectares, 1m

2

=

10000

1

hectares

∴9,900m

2

=

10000

9900

=0.99 hectares

Now, Area of park excluding cross roads = Area of park−Area of road

=(AB×AD)−9,900

=(700×300)−9,900

=2,10,000−9,900

=2,00,100 m

2

=

10000

200100

hectares=20.01 hectares.

Answer 2

Here, PQ=10m and PS=300m, EH=10m and EF=700m

And KL=10m and KN=10m

Area of roads = Area of PQRS+Area of EFGH−Area of KLMN

[∵ KLMN is taken twice, which is to be subtracted]

=PS×PQ+EF×EH−KL×KN

=(300×10)+(700×10)−(10×10)

=3000+7000−100

=9,900m

2

Area of road in hectares, 1m

2

=

10000

1

hectares

∴9,900m

2

=

10000

9900

=0.99 hectares

Now, Area of park excluding cross roads = Area of park−Area of road

=(AB×AD)−9,900

=(700×300)−9,900

=2,10,000−9,900

=2,00,100 m

2

=

10000

200100

hectares=20.01 hectares.