Question

The base of a triangular field is three times its height. if the cost of cultivating the field at 1080 per hectare is 14580, find its base and height

Answer 1

Let height = h
Therefore, base = 3h
Area = 1/2*b*h
1/2*3h*h = 3h^2/2
3h^2/2 * 1080 = Rs. 14580
h^2 = 14580 * 2 / 3 = 9720 
h = sqrt(9720)  = 98.59m

Answer 2

Answer:

The base is 900 m and height is 300 m.

Step-by-step explanation:

Let the height of triangular field be h

Since we are given that The base of a triangular field is three times its height.

So, base = 3h

Area of triangular field = 1/2 *Height*Base =1/2*h*3h=3h^2/2

Area cultivated for cost rs.1080 = 1 hectare =10000 sq.m.

Area cultivated for cost rs.1= 10000/1080 sq.m.

Area cultivated for cost rs.14580= (10000/1080)*14580 sq.m.

                                                      =135000 sq.m.

So, area of triangular field = 135000 sq.m.

So, 3h^2/2=135000

3h^2=135000 *2

3h^2=270000

h^2=270000/3

h^2=90000

h= 300 m

Thus the height is 300 m.

Base = 3h =3*300=900m

Hence the base is 900 m and height is 300 m.