Question

A rectangular park is 50 m long and 30 m broad. Find the cost of:

(a) fencing the park at ₹ 2.50 per m.

(b) levelling the park at ₹ 5.50 per sq. m.​

Answer 1

AnswerS

✳The cost of fencing the rectangular park = ₹400.

✳ The Cost of leveling the park = ₹ 8250.

SOLUTION

Length of the rectangular park = 50m.

Breadth of the rectangular park = 30m.

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Fencing

Fencing is done along the edge of the park.

Perimeter of rectangle = 2(l+b) , Where l is length and b is breadth of the rectangle .

Here,

l = 50m.

b = 30m.

$\implies$ Perimeter = 2(50+30)

$\implies$ Perimeter = 2 × 80

$\implies$ Perimeter of the rectangular park = 160 m.

Cost of fencing = Rate of fencing × Perimeter of the park

Rate of fencing =  ₹ 2.50/m.

$\implies$ Cost of fencing = 2.50 × 160

The cost of fencing the rectangular park = ₹400.

Leveling

Leveling is done inside the rectangular park.

Area of the rectangle = l × b , Where l is length and b is breadth of the rectangle .

Here,

l = 50m.

b = 30m.

$\implies$ Area = 50 × 30

$\implies$ Area of the rectangular park  = 1500m².

Cost of leveling = Rate of leveling × Area of the park

Rate of leveling = ₹ 5.50/m².

$\implies$ Cost of leveling = 5.50 × 1500

The Cost of leveling the park = ₹ 8250.

Answer 2

• Cost of fencing = ₹400.
• Cost of levelling = ₹8250.

Step-by-step explanation:

Given-

• Length= 50 m
• Breadth = 30 m.

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To find-

• (a) Cost of fencing (through perimeter)
• (b) Cost of levelling (through area).

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Solution -

(a) fencing the park at ₹ 2.50 per m.

$\bold\red{➠}$ To find the cost of fencing, we'll first have to find the perimeter of the rectangular park as fencing is done on the borders of any field.

$\underline{\boxed{\sf\orange{Perimeter_{(rectangle)} = 2(length+breadth)}}}$

$2(50 + 30) \\ \\ = 2 \times 80 \\ \\ = 160 \: m$

So, perimeter = 160 m.

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$\bold\red{➠}$Let's find the total cost of fencing.

$160 \times 2.50 \\ \\ = \frac{160}{1} \times \frac{250}{100} \\ \\ = 16 \times 25 \\ \\ = 400$

So, cost of fencing the rectangular park is $\tt\red{₹400}$

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(b) levelling the park at ₹ 5.50 per sq. m.

$\bold\blue{➠}$ So now to find the total cost of levelling the park, we'll first have to find the area as the levelling is done on the surface area of the park.

$\underline{\boxed{\sf\orange{Area_{(rectangle)} = length×breadth}}}$

$50 \times 30 \\ \\ = {1500 \: m}^{2}$

So, area= ${1500\:m}^{2}$

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$\bold\blue{➠}$Let's find the total cost of levelling the rectangular park.

$1500×5.50\\ \\= \frac{1500}{1}×\frac{550}{100}\\ \\=15×550\\ \\= 8250$

So, the cost of levelling of the rectangular park $\tt\blue{₹8250}$

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