Question

The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m² is ₹ 49,572; find its base and height.

Answer 1

Since the cost of cultivating the field at the rate of Rs. 36.72 per 100 square metre is Rs. 49,572.

Area of the triangular field = `(49572 xx 100)/36.72` = 1,35,000 sq. m

Let the height of the triangle be h.

Now,

Area of the triangular field = `1/2` × base × height

1,35,000 = `1/2 xx h xx 3h`

⇒ h² = 90,000
⇒ h = 300

Height (h) = 300m
Base (3h) = 3 × 300 = 900 m.