Question

Prakash has a rectangular field whose length and breadth are in the ratio 5:3. He wants to fence the field barbed wire. If the cost of fencing the field at the rate of RS. 15 per metre is RS. 9600, find the dimensions of the field.

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Answer 1

Step-by-step explanation:

Given:-

• The length and breadth of a rectangular field are in the ratio 5:3.

• The cost of fencing the field at the rate of RS. 15 per metre is RS. 9600.

To Find:-

• The dimensions of the field (Length and breadth)

Solution:-

Total cost of fencing the field = Rs.9600

Cost of fencing the field per metre = Rs.15

$\sf Perimeter\: of \:the\: field = \dfrac{Total\: cost}{Cost\: per \: m}$

$\sf = \dfrac{9600}{15}$

$\sf = 640$

$\sf \therefore \underline{Perimeter \: of\: the\: field = 640m}$

The length and breadth of a rectangular field are in the ratio 5:3.

Let the length be 5x and breadth be 3x

Perimeter of the rectangle = 2(Length + Breadth)

$\sf \longrightarrow 2(Length + Breadth) = 640$

$\sf \longrightarrow 2(5x + 3x) = 640$

$\sf \longrightarrow 2 \times 8x = 640$

$\sf \longrightarrow 16x= 640$

$\sf \longrightarrow x = \dfrac{640}{16}$

$\sf \longrightarrow x = 40$

• 5x = 5 × 40 = 200

• 3x = 3 × 40 = 120

Therefore:-

Length of the field = 200m

Breadth of the field = 120m

Answer 2

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