The base of a triangular field is twice its altitude. If the cost of cultivating the field at ₹ 14.50 per 100 m² is ₹ 52,200, find its base and altitude.

Given,

Rate of cultivation = ₹14.50 per 100 m²

= ₹ $\dfrac{14.50}{100}$ per m².

Total cost = ₹52,200

$\Rightarrow \text{Total cost} = \text{Area } \times \text{ Rate of cultivation} \\[1em] \Rightarrow 52,200 = \text{Area } \times \dfrac{14.50}{100} \\[1em] \Rightarrow Area = \dfrac{52200 × 100}{14.50} \\[1em] \Rightarrow Area = \dfrac{5220000}{14.50} \\[1em] \Rightarrow Area = 360000 \text{ m}^2. \\[1em]$

Let altitude be x meters and base be 2x meters.

We know that,

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

⇒ 360000 = $\dfrac{1}{2}$ × 2x × x

⇒ x² = 360000

⇒ x = 600.

∴ Altitude = x = 600 m and Base = 2x = 2 × 600 = 1200 m.

Hence, altitude = 600 m and base = 1200 m.