Question

6. A rectangular lawn measuring 50m by 36m is surrounded externally by a path which is 2m wide. Find the
area of the path also calculate the cost of leveling of the path at Rs.20 per m2​

Answer 1

Given:

• The length of a rectangular lawn is 50m
• The breadth of the rectangular lawn is 36m
• It is surrounded externally by a path which is 2m wide.

To find:

• The area of the path
• And the cost of levelling the path at Rs 20 per m sq.

So,

According to the question, image is attached

So,

• PQRS is the rectangle with length 50m and breadth 36m

Area of the rectangle PQRS = (l*b) unit sq.

Area of the rectangle PQRS = (50*36) m sq.

Area of the rectangle PQRS = 1800 m sq.

Now,

• ABCD is the rectangle with length (50+2+2) = 54m and breadth (36+2+2) = 40m, by adding the 2m wide path.

Area of the rectangle ABCD = (l*b) unit sq.

Area of the rectangle ABCD = (54*40) m sq.

Area of the rectangle ABCD = 2160 m sq.

So,

Area of the 2m wide path = [area of rectangle ABCD - Area of rectangle PQRS]

Area of 2m wide path = 2160 - 1800

Area of 2m wide path = 360 m sq.

Now,

The cost of levelling 1 m sq = Rs 20

Then,

Cost of levelling 360 m sq = 20*360 = Rs.7200

Hence

• The cost of levelling the 2m wide park is 7200

Answer 2

Answer:

Given :-

• Length = 50 m
• Breadth = 36 m
• It is surrounded by 2 m wide path

To Find :-

• Area of path at Cost of levelling at ₹20 per m²

Solution :-

As we know that

Area of Rectangle = L × B

Area of lawn = 50 × 36

Area of lawn = 1800 m²

Now,

When 2 m added to all sides

Length = (50 + 2 + 2) = 54 m

Breadth = (36 + 2 + 2) = 40 m

Now,

New Area = 54 × 40

Area = 2160 m²

Now,

Area of path = 2160 - 1800

Area of path = 360 m²

Total cost = 360 × ₹20

Total cost = ₹7200