Question

The base of a triangular field is three times its altitude if the cost of cultivating the field at Rs.240 per hectare Rs.3240 find its base height

Answer 1

Answer :-

• The height of the triangle = 300 m

• The base of the triangle = 900 m

Given :-

⁃ The base of a triangular field is three times its altitude.

⁃ The cost of cultivating the field at Rs.240 per hectare Rs.3240.

To find :-

‣ The base of the triangle

‣ The height (or altitude) of the triangle

Formula Used :-

$\tt{\mapsto Area\:\:of\:\:the\:\:triangle = \dfrac{1}{2}\times\: Base\times\: Height}$

Solution :-

Rs. 240 is the cost of cultivating $\longrightarrow$ 1 hectare

$\tt{Rs.\:3240\:\:is\:\:the\:\:cost\:\:of\:\:cultivating}\longrightarrow \:\: \dfrac{1 \times \: Rs.\:3240}{Rs.\:240}= \:\: 13.5 \:hectare$

As we know that,

1 hectare = 10000 m²  

13.5 hectares = 13.5 × 10000 m² = 135000 m²

∴ Area of the triangle = 135000 m²

Let the height of the triangle be h.

Then, the base of the triangle = 3h

Substituting the values we have in the area formula,

$\tt{\mapsto\:Area\:\:of\:\:the\:\:triangle = \dfrac{1}{2}\times\: 3h\times\: h}\\\\\tt{\mapsto\:135000 m^{2} = \dfrac{3h^{2} }{2}}\\\\\tt{\mapsto\:90000 m^{2} =h^{2}}\\\\\tt{\mapsto\:\sqrt{90000 m^{2}}=h}\\\\\tt{\mapsto\:300\:m=h}$

The height of the triangle = h = 300 m

The base of the triangle = 3h = 3 × 300 m = 900 m