The base of a triangular field is 3 times its height. If the cost of cultivating the field at the rate of ₹25 per 100 m² is ₹60000, find its base and height.

Given,

Cost of cultivating the field at the rate of ₹25 per 100 m² = ₹ 60000

In ₹25, area of field cultivated = 100 m²

∴ In ₹60000, area of field cultivated = $\dfrac{100 \times 60000}{25}$ = 240000 m².

∴ Area of field = 240000 m².

Let base of field = b meters and height = 3b meters.

Area of triangle = $\dfrac{1}{2} \times$ base × height

Substituting values we get,

$\Rightarrow 240000 = \dfrac{1}{2} \times b \times 3b \\[1em] \Rightarrow 240000 = \dfrac{3b^2}{2} \\[1em] \Rightarrow b^2 = \dfrac{240000 \times 2}{3} \\[1em] \Rightarrow b^2 = 160000 \\[1em] \Rightarrow b = \sqrt{160000} = 400 \text{ m} \\[1em] \Rightarrow \text{height } = 3b = 3 \times 400 = 1200 \text{ m}.$

Hence, base = 400 m and height = 1200 m.