Question

The base of a triangular field is twice its altitude. If the cost of cultivating the field at ₹ 14.50 per 100cm^2 is ₹ 52200, find its base and altitude.​

Answer 1

Let altitude of the triangular field be h m

Then base of the triangular field is 3h m.

Area of the triangular field = 12×h×3h=3h22m2..........(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,

3h22=135000 m2

3h2 = 135000 x 2 = 270000 m2

h2 = 270000 3m2=90000 m2 = (300 m)2

⇒ h = 300 m

Hence,

Height of the triangular field = 300 m and base of the triangular field = 3 x 300 m = 900 m