The base of a triangular field is three times | vedclass

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(A) Area of the field $= \frac{	ext{Total cost}}{	ext{Rate}} = \frac{675}{50} = 13.5 	ext{ hectares}$.Since $1 	ext{ hectare} = 10,000 \, m^2$,the

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$900 \, m$ and $300 \, m$

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(A) Area of the field $= \frac{	ext{Total cost}}{	ext{Rate}} = \frac{675}{50} = 13.5 	ext{ hectares}$.Since $1 	ext{ hectare} = 10,000 \, m^2$,the area is $13.5 	imes 10,000 = 135,000 \, m^2$.Let the altitude be $x \, m$. Then the base is $3x \, m$.The area of a triangle is given by $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{altitude}$.So,$\frac{1}{2} 	imes 3x 	imes x = 135,000$.$\frac{3x^2}{2} = 135,000$.$3x^2 = 270,000$.$x^2 = 90,000$.$x = 300 \, m$ (Altitude).Base $= 3x = 3 	imes 300 = 900 \, m$.

The base of a triangular field is three times its altitude. If the cost of cultivating the field at $50$ per hectare is $Rs. 675$,then what are its base and height?

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