Question

If the length of a rectangular farm and its breadth are in the ratio 5 : 4 and the area of the farm is 13520 m², find the cost of fencing the farm at the rate of 15 per metre.
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Answer 1

Answer:

Rs 7020

Step-by-step explanation:

Let the length and breadth be 5x and 4x respectively.

Area of rectangle =  length × breadth

⇒ 13520 = (5x) × (4x)

⇒ 13520 = 20x²

⇒ 13520/20 = x²

⇒ 676 = x²

⇒ √676 = 26 = x

Perimeter of the farm = 2(length + breadth)

                  = 2(5x + 4x)

                  = 2(9x) = 18x

                  = 18(26) = 468

∴ Cost of fencing = rate x perimeter

                    = Rs 15 x 468

                    = Rs 7020

Answer 2

Given :-

Ratio of length and breadth 5:4

Area = 13520 m²

Rate = 15 per m

To Find :-

Cost of fencing

Solution :-

$\sf Area = l \times b$

Let the sides be 5x and 4x

$\sf 13520 = 5x \times 4x$

$\sf 13520 = 20x^{2}$

$\sf \dfrac{13520}{20} = x^{2}$

$\sf 676 = x^{2}$

$\sf \sqrt{676} = x$

$\sf 26 =x$

Length = 5(26) = 130 m

Breadth = 4(26) = 104 m

Perimeter = 2(130 + 104)

Perimeter = 2(234)

Perimeter = 468 m

Cost = Perimeter  x Rate

Cost = 468  x 15

Cost = Rs 7020