A rectangular field is 100 m long and 80 m wide. A path 10 m wide path is to be
m wide. A path 10 m wide path is to be built inside the field all
along its border. Find the area of the path.
um 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.
3. A square lawn is surrounded by a 5 m wide path. If the area of the path is 400 m-, find the area of the law.
4. A room is 20 m long and 15 m broad. It has to be carpeted after leaving a margin of 2 m all around it. Find
the area of the carpet required and the cost of carpeting it at 800 per m.
5. A piece of cloth is 5 m long and 2 m wide. A border of width 50 cm has to to printed and stitched all around
it on the outside. Find the cost of printing the border at 200 per m².
6. A rectangular lawn 100 m long and 70 m broad has two crossroads running in the middle of it—one 2 m
wide running parallel to its length and the other 5 m wide running parallel to its breadth. Find the area of
the lawn not covered by the crossroads.
7. A piece of cloth is 70 cm long and 50 cm wide, A strip of width 10 cm is cut from all around it. Find the
area of the remaining cloth and the area of the strip..
8 A mirror of length 30 cm and width 20 cm is to beframed with a 2 cm wide frame. Find the area of the
frame required. Also find the cost of framing at the rate of 20 per cm².
Answers
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.
Answer:
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.