A lawn is in the form of a triangle having it | vedclass

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(B) Let the base of the triangle be $2x\, m$ and the height be $3x\, m$.The area of a triangle is given by $\frac{1}{2} 	imes 	ext{base} 	imes 	ex

Vedclass · Accepted Answer

$33\frac{1}{3}\, m, 50\, m$

Vedclass · Answer

(B) Let the base of the triangle be $2x\, m$ and the height be $3x\, m$.The area of a triangle is given by $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Given that $1\, 	ext{hectare} = 10000\, m^2$,the area of the lawn is $\frac{1}{12} 	imes 10000 = \frac{10000}{12} = \frac{2500}{3}\, m^2$.Setting up the equation: $\frac{1}{2} 	imes (2x) 	imes (3x) = \frac{2500}{3}$.$3x^2 = \frac{2500}{3}$.$x^2 = \frac{2500}{9}$.$x = \sqrt{\frac{2500}{9}} = \frac{50}{3}$.Base $= 2x = 2 	imes \frac{50}{3} = \frac{100}{3} = 33\frac{1}{3}\, m$.Height $= 3x = 3 	imes \frac{50}{3} = 50\, m$.

$A$ lawn is in the form of a triangle having its base and height in the ratio $2:3$. The area of the lawn is $\frac{1}{12}$ hectare. Find the base and height of the lawn.

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