Question

. The length and breadth of a park are in the ratio 2:1 and its perimeter is 240 m. A path
2 m wide runs inside it, along its boundary. Find the cost of paving the path at rupees 80 per m
.​

Answer 1

Answer:

Rs 37,120

Step-by-step explanation:

Let the length and the breadth of the park be 2x m and x m, respectively.

Perimeter of the park = 2(2x + x) = 240 m

⇒ 2(2x + x) = 240

⇒ 6x = 240

⇒ x =  m =40 m

∴ Length of the park = 2x = (2 × 40) = 80 m

Breadth = x = 40 m

Let PQRS be the given park and ABCD be the inside boundary of the path.

Length = 80 m

Breadth = 40 m

Area of the park = (80 ×40) m2 = 3200 m2

Width of the path = 2 m

∴ AB = (80 - 2 × 2) m = (80 - 4) m =76 m

 AD = (40 - 2  × 2) m = (40 - 4) m = 36 m

Area of the rectangle ABCD = (76 × 36) m2 = 2736 m2

Area of the path = (Area of PQRS - Area of ABCD)

                           = (3200 - 2736) m2 = 464 m2

Rate of paving the path = Rs. 80 per m2

∴ Total cost of  paving the path = Rs. (464×80) = Rs. 37,120

Answer 2

Question

The length and breadth of a park are in the ratio 2:1 and its perimeter is 240 m. A path 2 m wide runs inside it, along its boundary. Find the cost of paving the path at rupees 80 per m

Given

• Length and Breadth of the park are in the ratio 2 : 1
• Perimeter 240m
• A path is 2m wide inside it ong it's boundary

Find

• Total cost of paving at the rate of ₹ 80 /m

Calculation

Let,

• The length be 2x and breadth be 1x
• Perimeter = 2 ( lenght + breadth )

$\sf ✒ \:240= 2 ( 2x + 1x )$

$\sf ✒ \: 240 = 2(3x)$

$\sf ✒ \:240 = 6x$

$\sf ✒ \: \dfrac{\cancel{240}}{\cancel{6}}=x$

$\sf ✒ \: x = 40m$

• breadth = x = 40 m
• Length = 2x = 2 × 40 = 80m

______________________________

$\bf{\underline{\boxed{\red{Area \:of \:outer\: park = Length × Breadth }}}}$

$\sf ✈ \: Area_{(outer\:park)}= 40×80$

$\sf ✈ \: Area_{(outer\:park)}=3200m^2$

Now,

$\sf ✦\: Area_{(inner\:park)}=(40-4)(80-4)$

$\sf ✦ \: Area_{(inner\:park)}=36×76$

$\sf ✦ \: Area_{(inner\:park)}= 2736m^2$

$\bf{\underline{\boxed{\red{Area \:of \:path= inner\:area-outer\:area }}}}$

$\sf ✈\: Area\:of\:path = 3200-2736m^2$

$\sf ✈\: Area\:of\:path = 464m^2$

Hence

• Cost of paving

$\sf ✒ \:Cost_{(paving)}=464×80$

$\sf ✒\: Cost_{(paving)}=37,120 \:rupee$