The base of a triangular field is three times its altitude. If the cos

1.	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» Let altitude of the triangular field be h m Then base of the triangular field is 3h m. We know that area of triangle = ½ x b x h Area of the triangular field = ½ (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

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»

Let altitude of the triangular field be h m

Then base of the triangular field is 3h m.

We know that area of triangle = ½ x b x h

Area of the triangular field = ½ (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