The length and breadth of a rectangular field | vedclass

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Question

(C) The cost of cultivation is given as ₹ $6000$ at a rate of $25$ $paise$ per square metre.Since $100$ $paise = ₹ 1,$ the rate is $0.25$ ₹ per $m^2$.

Vedclass · Accepted Answer

$200 \, m, 120 \, m$

Vedclass · Answer

(C) The cost of cultivation is given as ₹ $6000$ at a rate of $25$ $paise$ per square metre.Since $100$ $paise = ₹ 1,$ the rate is $0.25$ ₹ per $m^2$.Area of the field $= \frac{	ext{Total Cost}}{	ext{Rate}} = \frac{6000}{0.25} = 24000 \, m^2$.Let the length be $5x$ and the breadth be $3x$.The area of a rectangle is $	ext{length} 	imes 	ext{breadth}$.So,$5x 	imes 3x = 24000$.$15x^2 = 24000$.$x^2 = \frac{24000}{15} = 1600$.$x = \sqrt{1600} = 40$.Therefore,the length $= 5 	imes 40 = 200 \, m$ and the breadth $= 3 	imes 40 = 120 \, m$.

The length and breadth of a rectangular field are in the ratio $5: 3.$ If the cost of cultivating the field at $25$ $paise$ per square metre is ₹ $6000,$ then find the dimensions of the field.

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