Question

The cost of the laying grass in a rectangular park at rs 5 per square metre is rs 2400 . Find the costing of making its boundary at rs 2.25 Per meter if its 15 m wide .
Pls show the workings

Answer 1

➤ Given :-

Cost of laying grass (per metre) :- ₹5

Cost of laying grass (whole park) :- ₹2400

Breadth of the park :- 15 metres

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➤ To Find :-

Rate of fencing it's boundary

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★ How to do :-

Here, we are given that a rectangular park is laid with grass at ₹5 per metre and ₹2400 is spent for laying the grass of whole park. The breadth is also given which measures 15 metres. So, we should find the cost of fencing it at ₹2.25 per metre. So, first we should find it's area by dividing the cost of laying grass for whole park and cost of laying grass per metre. Then, we should find the length of the park by dividing area and breadth. Then, we can find the perimetre of the park using the length and the breadth. Finally, we can find the cost of fencing it by multiplying the perimetre and the cost of fencing per metre.

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➤ Solution :-

Area of the park :-

${\tt \leadsto \dfrac{2400}{5}}$

${\tt \leadsto \cancel \dfrac{2400}{5} = 480 \: \: Metres^{2}}$

Length of the park :-

${\tt \leadsto \dfrac{480}{15}}$

${\tt \leadsto \cancel \dfrac{480}{15} = 32 \: \: Metres}$

Perimeter of the park :-

${\tt \leadsto 2 \: (32 + 15)}$

${\tt \leadsto 2 \: (47) = 2 \times 47}$

${\tt \leadsto 94 \: \: Metres}$

Now,

Cost of fencing the whole park :-

${\tt \leadsto 94 \times 2.25}$

${\tt \leadsto \boxed{\tt Rs \: \: 211.5}}$

$\Huge\therefore$ The cost of fencing the whole park is ₹211.5.

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$\dashrightarrow$ Some related formulas :-

${\sf \to Perimetre_{(rectangle)} :- 2 \: (Length + Breadth)}$

${\sf \to Area_{(rectangle)} :- Length \times Breadth}$

${\sf \to Length_{(rectangle)} :- \dfrac{Perimetre}{2} - Breadth}$

${\sf \to Breadth_{(rectangle)} :- \dfrac{Perimetre}{2} - Length}$

${\sf \to Length_{(rectangle)} :- \dfrac{Area}{Breadth}}$

${\sf \to Breadth_{(rectangle)} :- \dfrac{Area}{Length}}$

Answer 2

Answer:

The cost of making  boundary= Rs 211.50

Step-by-step explanation:

★ Given :

A rectangular park with 15 m width.The cost of the laying grass in the park at Rs 5 per square metre is Rs 2400.

★ To find :

The cost of making its boundary at Rs 2.25 / m

★ Solution:

• The rate of laying grass= Rs 5/m²
• Total cost= Rs 2400
• Thus Area =  $\frac{Total cost}{Rate}$=$\frac{2400}{5} =Rs 480$

Now Given width =15 m

Length =$\frac{Area}{width} = \frac{480}{15} = 32 m$

Now Parameter of the park=2 x ( length + width)

=2 x ( 32+15) =2 x 47 =94 m

Rate of boundary = Rs 2.25 / m

Total cost= Perimeter x Rate

=94 x 2.25 = Rs 211.50

★ Answer:

The cost of making  boundary= Rs 211.50

★ Formulas and concept used:

For a rectangle with length a , width b and area A

1. Area A =  a x b
2. Length a = $\frac{A}{b}$  
3. Perimeter P=2 x (a+b)

★ Other important formulas for Rectangle and square:

1. Diagonal of a rectangle =$\sqrt{a^{2} + b^{2} }$
2. Area of a square = side²
3. Side of a square =$\sqrt{Area}$  
4. Perimeter of a square = 4 x side
5. Diagonal of a square = side $\sqrt{2}$