Question

The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs 24.60 per hectare is Rs 332.10, find its base and height.

Answer 1

Let altitude of the triangular field be h m

Then base of the triangular field is 3h m.

We know that area of triangle = x b x h

Area of the triangular field = (h x 3h) = 3h2/2 m2 ……. (i)

The rate of cultivating the field is Rs 24.60 per hectare.

Therefore,

Area of the triangular field = 332.10 /24.60

= 13.5 hectare

= 135000 m2 [Since 1 hectare = 10000 m2] …… (ii)

From equation (i) and (ii) we have,

3h2/2 = 135000 m2

3h2 = 135000 x 2 = 270000 m2

h2 = 270000/3

= 90000 m2

= (300)2

h = 300 m

Hence, Height of the triangular field = 300 m and

Base of the triangular field = 3 x 300 m = 900 m