Question

find the cost of cementing the path​

Answer 1

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Length of park=50 m

Breadth=36

Area=50×36=1800 m²

Area of park including a 4 m wide path

Length=50+4=54 m

Breadth=36+4=40 m

Area=54×40=2160 m²

Area of path= 2160-1800=360

So area of path is 360m²

Cost of cementing 1m²=₹400

Cost of cemeting the path= 360× 400 = ₹144000

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Answer 2

Question:

A rectangular park is 50 m long and 36 m board. A path for 4 m broad is running outside the rectangular park, along its boundary. Find the cost of cementing the path at the rate of Rs. 400 per 10 m².

How to solve?

Here, in this question first we will find the area of rectangular park ( area of original rectangle ) i.e., ABCD then, we will find area of the rectangle formed after making the path. After that we will substract area of original rectangle from area of the rectangle formed after making the path, the result is equal to the area of path. After finding area of path - we will find it's cost.

Solution:

Let ABCD be the rectangular park and,

EFGH be the area of the rectangle formed after making the path.

AB = 50 m

BC = 36 m

Area of rectangle = l × b

• Area of rectangle ABCD = l × b

• Area of rectangle ABCD = 50 × 36

• Area of rectangle ABCD = 1800 m²

Area of rectangular park = 1800 m²

Now for finding area of EFGH, we will first find length of EF and HG or in other words we will find length and breadth of EFGH.

⇛EF = 50 + 4 + 4

⇛EF = 54 + 4

⇛EF = 58 m = lenth

⇛HG = 36 + 4 + 4

⇛HG = 40 + 4

⇛HG = 44 m = breadth

Area of rectangle = l × b

• Area of rectangle EFGH = l × b

• Area of rectangle EFGH = 58 × 44

• Area of rectangle EFGH = 2552 m²

Area of the rectangle formed after making the path = 2552 m²

• Area of path = Area of rectangular park - Area of the rectangle formed after making the path

• Area of path = lb - lb

• Area of path = ( 2552 - 1800 ) m²

• Area of path = 752 m²

Area of a path = 752 m²

Now, let's find out cost.....

➨ Cost of cementing 10 m² of the path = Rs. 400

➨ Cost of cementing 1 m² of the path = 400/10

➨ Cost of cementing 1 m² of the path = Rs. 40

Now, we will find the cost of cementing the path by using simple unitary method....

➨ Cost of cementing the path = Rs. 40 × 752

➨ Cost of cementing the path = Rs. 30,080

The cost of cementing the path = Rs. 30,080

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