The base of a triangular field is three times | vedclass

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(C) The cost of cultivation is ₹ $495.72$ at a rate of ₹ $36.72$ per hectare.Area of the field in hectares $= \frac{495.72}{36.72} = 13.5 	ext{ hecta

Vedclass · Accepted Answer

$900 \, m, 300 \, m$

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(C) The cost of cultivation is ₹ $495.72$ at a rate of ₹ $36.72$ per hectare.Area of the field in hectares $= \frac{495.72}{36.72} = 13.5 	ext{ hectares}$.Since $1 	ext{ hectare} = 10,000 \, m^2$,the area in square meters is $13.5 	imes 10,000 = 135,000 \, m^2$.Let the height of the triangular field be $h = x \, m$.Then,the base $b = 3x \, m$.The area of a triangle is given by $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = 135,000$.$\frac{1}{2} 	imes 3x 	imes x = 135,000$.$1.5x^2 = 135,000$.$x^2 = \frac{135,000}{1.5} = 90,000$.$x = \sqrt{90,000} = 300$.Therefore,height $= 300 \, m$ and base $= 3 	imes 300 = 900 \, m$.

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ $36.72$ per hectare is ₹ $495.72$,then find its base and height.

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