Question

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 1

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.

Answer 2

Answer:

Given:

• The base of a triangular field is thrice its altitude if the cost of cultivating it at ₹246.80 per hectare is ₹3331.80.

Find:

• Find its base and height.

Know terms:

• (b) = Base.

• (h) = Height.

Calculations:

⇒ 3331.80 = [246.80 × Area]

⇒ Area = [3331.80/246.80]

Using formula: Area of triangle:

⇒ [1/2 × b × h]

Finding the height of the triangle:

⇒ 3331.80/246.80 = 1/2 × b × h

⇒ 1110.6/123.4 = h²

⇒ 9 = h²

⇒ √9 = h

⇒ 3 = h

Therefore, 3 is height of the triangle.

Finding the base of the triangle:

⇒ b = 3 (3)

⇒ b = 9

Therefore, 9 is base of the triangle.