Question

The area of a rectangular park is 1560 m square and its breadth is 24 m. Find the length and perimeter of the park. Also, find the cost of fencing it at $ 22.50 per metre. ​

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { {Answer:}} }} }$

• Length = 65 m
• Cost of fencing = $ 4005

$\underline{ \underline{\Large \pmb{\sf { {Given:}} }} }$

• Area of the rectangular park = 1560 m²

• Breadth = 24 m

• Cost of fencing per m = $ 22.50

$\underline{ \underline{ \Large \pmb{\sf { {To \: calculate:}} }} }$

• Total cost of fencing the park.

$\underline{ \underline{ \Large \pmb{\sf { {Calculation:}} }} }$

As we know that, fencing is done on the border of the particular object. Border is also called the perimeter. Therefore, in order find the total cost of fencing the park, we need to calculate its perimeter.

To calculate the perimeter of the park, we need to find its length.

✰ Calculating length of the park :

$\bigstar \:\boxed{\sf{ {Area}_{(Rectangle)} = Length \times Breadth }}$

$\longrightarrow \sf { 1560 = Length \times 24}$

$\longrightarrow \sf { \dfrac{1560}{24} = Length }$

$\longrightarrow\underline{\boxed{\sf{65 \: m = Length }}} \: \red{\bigstar}$

Henceforth,

• Length of the park is 65 m.

✰ Calculating perimeter of the park :

$\bigstar \: \boxed{\sf { {Perimeter}_{(Rectangle)} = 2 ( Length + Breadth) }}$

$\longrightarrow\sf {Perimeter_{(Rectangle)} = 2 ( 24 + 65) \: m }$

$\longrightarrow \sf{ Perimeter_{(Rectangle)} = 2 (89) \: m }$

$\longrightarrow\underline{\boxed{\sf{ {Perimeter}_{(Rectangle)} = 178 \: m }}} \: \red{\bigstar}$

Henceforth,

• Perimeter of the park is 178 m.

✰ Calculating the cost of fencing :

$\bigstar \: \boxed{\sf{ {Cost \: of \: fencing}_{(1 \: {m}^{2} )} = 22.50 \: Dollars }}$

$\longrightarrow \sf{{Cost \: of \: fencing}_{(Park )} = ( 22.50 \times 178) \: Dollars }$

$\longrightarrow \sf{{Cost \: of \: fencing}_{(Park )} = ( 22.5 \times 178) \: Dollars }$

$\longrightarrow \sf{{Cost \: of \: fencing}_{(Park )} = ( \dfrac{225}{10} \times 178) \: Dollars }$

$\longrightarrow \sf{{Cost \: of \: fencing}_{(Park )} = ( \dfrac{45}{2} \times 178) \: Dollars }$

$\longrightarrow \sf{{Cost \: of \: fencing}_{(Park )} = ( 45 \times 89) \: Dollars }$

$\longrightarrow \underline{\boxed{\sf{ {Cost \: of \: fencing}_{(Park )} = 4005 \: Dollars }}} \: \red{\bigstar}$

Therefore,

• Total cost of fencing the park is $ 4005.

Answer 2

Given :

• Area of a rectangular park = 1560m²
• Breadth of Park = 24m
• Rate of Fencing = $22.50 per m

To Find :

• Length of Park
• Perimeter of Park
• Cost of Fencing the Park

Solution :

⟾ Length of the Park :

• Area of Park = Length × Breadth
• 1560 = Length × 24
• 1560 / 24 = Length
• 65m = Length of Park

⠀

⟾ Perimeter of the Park :

• Perimeter = 2 (Length + Breadth)
• Perimeter = 2 ( 24 + 65 )
• Perimeter = 2 × 89
• Perimeter of Park = 178m

⠀

⟾ Cost of Fencing the Park :

• Cost of Fencing 1m of Park = 22.50
• Cost of Fencing 178m = 22.50 × 178
• Cost of Fencing 178m = $4005

________________

Therefore :

• Length of Park = 65m
• Perimeter of Park = 178m
• Cost of Fencing = $4005

________________