Question

Find the area of the following borders.
Inner length = 100 m, Inner breadth = 50 m, Width of the border = 2 m​

Answer 1

Step-by-step explanation:

1) The area of the path is 3200 sq m.

length of field = 100m

breadth of field = 80 m

area of field = 8000 sq m

length of inside field = 100-10-10m = 80m

breadth of field = 80-10-10m = 60m

area of field = 4800 sq m

area of path = 8000 - 4800 sq m = 3200 sq m.

2) There is a garden inside a 150 m long and 100 m wide rectangular park. A 20 m wide path is built surrounding  the garden along the boundary of the park. Find the area of the garden.

The area of the garden is 3200 sq m.

length of park = 150m

breadth of park = 100 m

area of park = 15000 sq m

length of inside garden = 150-20-20m = 110m

breadth of inside garden = 100-20-20m = 60m

area of inside garden = 6600 sq m

3) the area of the lawn is 225 sq m

Let the length of the lawn be x metres

then the length of the boundary is (x + 5 + 5) metre = (x+10) metre

Area of lawn = x^2 sq m

area of lawn with path = (x+10)^2 sq m

area of path = 400 sq m  

        ⇒  (x+5)^2 - x^2 sq m = 400  

        ⇒  x^2 + 20x + 100 - x^2 = 400  

        ⇒ 20x + 100 = 400

        ⇒ x = 15m

Area of lawn = 15*15 sq m = 225 sq m.

4) the area of the carpet is 176 sq m and the cost is Rs 1,40,800

length of room = 20m

breadth of room = 15m

length of carpet = 20-2-2m = 16m

breadth of carpet = 15-2-2m = 11m

area of carpet = 176 sq m

cost of carpeting = Rs 176 * 800 = Rs 1,40,800

5) the cost is Rs 1600

length of cloth = 5m

breadth of cloth = 2 m

area of cloth = 10 sq m

length of  cloth with border= 5+0.5+0.5m = 6m

breadth of cloth with border= 2+0.5+0.5m = 3m

area of cloth with border = 18 sq m

area of border = 18-10 sq m = 8 sq m.

cost = 8*200 rs = 1600rs.