the base of a triangular field is thrice its altitude if the cost of c

1.	the base of a triangular field is thrice its altitude if the cost of cultivating it at ₹ 246.80 per hectare is ₹ 3331.80 then find its base and height
Answer» Solution : $\bf{\blue{\underline{\underline{\bf{Given\::}}}}}$ The BASE of a triangular FIELD is thrice it's altitude if the cost of cultivating it at Rs.246.80 per hectare is Rs.3331.80. $\bf{\blue{\underline{\underline{\bf{To\:find\::}}}}}$ The base and height of triangular field. $\bf{\blue{\underline{\underline{\bf{Explanation\::}}}}}$ Let the base of triangle be 3r Let the height of triangle be R A/q $\implies\sf{3331.80=246.80\times Area}\\\\\\\implies\sf{Area= \dfrac{3331.80}{246.80} }$ We know that formula of the area of triangle : $\implies\bf{{Area\:of\:triangle=\dfrac{1}{2} \times base\times height}}\\\\\\\implies\sf{\dfrac{\cancel{3331.80}}{\cancel{246.80}} =\dfrac{1}{\cancel{2}} \times \cancel{3}r\times r}\\\\\\\implies\sf{\cancel{\dfrac{1110.6}{123.4}} =r^{2}} \\\\\\\implies\sf{9=r^{2} }\\\\\\\implies\sf{\sqrt{9} =r}\\\\\\\implies\sf{\red{3=r}}$ Thus; The height of the triangle is r = 3 UNITS. The base of triangular field is 3r = 3(3) = 9 units.

the base of a triangular field is thrice its altitude if the cost of cultivating it at ₹ 246.80 per hectare is ₹ 3331.80 then find its base and height

Answer»

Solution :

$\bf{\blue{\underline{\underline{\bf{Given\::}}}}}$

The BASE of a triangular FIELD is thrice it's altitude if the cost of cultivating it at Rs.246.80 per hectare is Rs.3331.80.

$\bf{\blue{\underline{\underline{\bf{To\:find\::}}}}}$

The base and height of triangular field.

$\bf{\blue{\underline{\underline{\bf{Explanation\::}}}}}$

Let the base of triangle be 3r

Let the height of triangle be R

A/q

$\implies\sf{3331.80=246.80\times Area}\\\\\\\implies\sf{Area= \dfrac{3331.80}{246.80} }$

We know that formula of the area of triangle :

$\implies\bf{{Area\:of\:triangle=\dfrac{1}{2} \times base\times height}}\\\\\\\implies\sf{\dfrac{\cancel{3331.80}}{\cancel{246.80}} =\dfrac{1}{\cancel{2}} \times \cancel{3}r\times r}\\\\\\\implies\sf{\cancel{\dfrac{1110.6}{123.4}} =r^{2}} \\\\\\\implies\sf{9=r^{2} }\\\\\\\implies\sf{\sqrt{9} =r}\\\\\\\implies\sf{\red{3=r}}$

Thus;

The height of the triangle is r = 3 UNITS.

The base of triangular field is 3r = 3(3) = 9 units.