Question

The length and breadth of a rectangular park is in the ratio 5:4. The cost of fencing the park at the rate of rupees 50 per metre will be rupees 4950. Find the length and breadth of the park.

Answer 1

Answer:

The length and breadth of the park are 27.5 m and 22 m respectively.

Step-by-step explanation:

Let the length and breadth of a rectangular park be 5x and 4x respectively.

Given:

Cost of fencing 1 m park = Rs 50

Let Cost of fencing y m park = Rs 4950

So, 1/y = 50/4950

→ y = 4950/50

→ y = 99

Formula: P = 2(l + b) unit

According to question:

2(5x + 4x) = 99

→ 2 × 9x = 99

→ 18x = 99

→ x = 5.5

∴ Dimensions of park:

Length = 5x = 5 × 5.5 = 27.5 m

Breadth = 4x = 4 × 5.5 = 22 m

Abbreviations used:

P = Perimeter of rectangle

l = Length of rectangle

b = Breadth of rectangle

Answer 2

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

➙ The dimensions of the park is :

• length = 27.5 metres
• breadth = 22 metres.

${\blue{\underline{\underline{\purple{\textsf{\textbf{Step-by-step explanation: }}}}}}}$

Given that,

The dimensions of a park is in ratio 5 : 4. The cost of fencing the park is ₹4,950 at the rate of ₹50 per metre.

Here, the rate and the total cost of fencing is given and also, dimensions are in the ratio.So,we need to find it's actual dimensions.

Step 1 :

Let's consider, the dimensions :

• Length = ‘5x’
• Breadth = ‘4x’

The park is in rectangle shape. Fencing of the park means the perimeter of the park.

We know that,

Perimeter of a rectangle = 2(l + b)

• l (length) = ‘5x’
• b (breadth) = ‘4x’

So,

→ 2(5x + 4x)

→ 2(9x)

→ 18x

Step 2 :

Perimeter of the rectangle is given by :

→ $\sf \frac{Total \: cost \: of \: fencing}{Rate \: of \: fencing }$

• Total cost of fencing is ₹4,950 (given)
• Rate is ₹50 per metre (given)

So,

→ $\sf \frac{4950}{50}$

→ 99 metres.

Step 3 :

Now we are getting two perimeters :

• One as variable i.e., ‘18x'
• As numerical i.e., ‘99 metres’

we can say that,

→ 99 = 18x

→ $\sf \frac{99}{18}$ = x

→ x = 5.5

∴ The value of ‘x’ is 5.5 metres

The dimensions are :

• length = 5x = 5(5.5) = 27.5 metres.
• breadth = 4x = 4(5.5) = 22 metres.