Question

Lendth and breath of a rectangle field is in the ratio of 9:5. Area of the field is 14580m². Find the cost of fence the field at a rate of Rs. 4.25 per metre.

Answer 1

Step-by-step explanation:

AppropriatE QuestioN :-

• The length and breadth of a rectangular field are in the ratio of 9 : 5. The area of the rectangular field is 14580 m². Then, find the cost of fencing the field at the rate of Rs. 4.25 per m².

GiveN :-

• The length and breadth of a rectangular field are in the ratio of 9 : 5.
• The area of the rectangular field is 14580 m².
• The cost of fencing the field per m² is Rs. 4.25.

To FinD :-

• The cost of fencing the rectangular field.

SolutioN :-

As per the information, we know that, we are given with the area and the ratio of length and breadth of the rectangular field. And, we are asked to find out the cost of fencing the field. In order to find the cost of fencing, it is necessary to have the measure of it's perimeter.

So, firstly, let us assume the measure of length of the field be 9x. So, the value of the measure of breadth of the rectangular field will be 5x, since the ratio of length and breadth of the field is 9 : 5. Through this, we'll find out the value of x by substituting the values in the formula of area of rectangle. And after that, we will find out the dimensions of the field. Let's do it !

• Area of the field = 14580 m²
• Length of the field = 9x
• Breadth of the field = 5x

$\rule{300}{2}$

$\sf \red \bigstar {\underline{Finding\ the\ value\ of\ x:-}}$

$\sf : \implies {Area\ of\ rectangle\ =\ length \times breadth} \\ \\ \sf : \implies {14580\ =\ 9x \times 5x} \\ \\ \sf : \implies {14580\ =\ 45x^2} \\ \\ \sf : \implies {\dfrac{\cancel{14580}}{\cancel{45}}\ =\ x^2} \\ \\ \sf : \implies {324\ =\ x^2} \\ \\ \sf : \implies {\sqrt{324}\ =\ x} \\ \\ \sf : \implies {18\ =\ x} \\ \\ : \implies {\underline{\boxed{\pink{\frak{x\ =\ 18}}}}}$

Hence, the required value of the x is 18. So, now we will find out the dimensions of the rectangular field.

$\rule{300}{2}$

LengtH :-

• Length = 9x
• 9 × 18
• 162 m

Hence, the required length of the rectangular field is 162 m. So, now we will find out the breadth of the field.

$\rule{300}{2}$

BreadtH :-

• Breadth = 5x
• 5 × 18
• 90 m

Hence, the required breadth of the rectangular field is 90 m. Now, we have the measures of the length and breadth. So, now we will find out the perimeter of the rectangular field.

$\rule{300}{2}$

$\sf \red \bigstar {\underline{Finding\ the\ perimeter\ of\ the\ rectangular\ field:-}}$

$\sf : \implies {Perimeter\ of\ rectangle\ =\ 2(length\ +\ breadth)} \\ \\ \sf : \implies {2(162\ +\ 90)} \\ \\ \sf : \implies {2 \times 252} \\ \\ : \implies {\underline{\boxed{\pink{\frak{504\ m}}}}}$

Hence, the perimeter of the rectangular field is 504 m. So, finally we will find out the cost of fencing the field.

$\rule{300}{2}$

$\sf \red \bigstar {\underline{Finding\ the\ cost\ of\ fencing\ the\ field:-}}$

$\sf \dashrightarrow {Perimeter\ of\ field \times Cost\ per\ m^2} \\ \\ \sf \dashrightarrow {504 \times 4.25} \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{Rs.\ 2142}}}}_{\scriptsize\blue {\sf{Cost\ of\ fencing}}}}$

Hence, the cost of fencing the rectangular field is Rs. 2142.

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Answer 2

Given :

• The length and breadth of a rectangular field are in the ratio 9:5.
• Area of the field =14580 sq m.
• Cost of fencing per meter ₹4.25.

To do :

• We have to find the cost of fencing the rectangular field.

Solution :

• Let the length and breadth of the field be 9x and 5x , respectively.

Let the length of the field be 9x and breadth be 5x.

• 9x × 5x=14580

• 45x²=14580

• x² = 324

• x=18

Hence, 

• length=162m and 
• breadth=90m.

• Perimeter = 2(l+b)
• 2(162+90)
• 2(252)=504m

Therefore,

• Cost of fencing = 504×4.25=2142

Hence, the cost of fencing the rectangular field is Rs. 2142.

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