The base of a triangular field is 2.4 times its height. If the cost of levelling the field at the rate of ₹ 20 per square metre is ₹ 9,600; find its base and height.

Given:

The cost of levelling the field = ₹9600

The rate of levelling = ₹20 per square metre

The base of the triangle is 2.4 times its height.

Let the height of the field be h meters.

Then base of the field = 2.4 x h.

As we know cost of levelling the field = Area of field x rate of levelling

⇒ 9600 = Area of field x 20

⇒ Area of field = $\dfrac{9600}{20}$ = 480

Area of triangular field = $\dfrac{1}{2}$ x base x height

⇒ $\dfrac{1}{2}$ x 2.4 x h x h = 480

⇒ 1.2 x h² = 480

⇒ h² = $\dfrac{480}{1.2}$

⇒ h² = 400

⇒ h = $\sqrt{400}$

⇒ h = 20 m

Base = 2.4 x h = 2.4 x 20 = 48 m

Hence, base of the field = 48 m and height = 20 m.