Question

The base of a triangular field is twice its height. If the cost of cultivating it at the
rate of Rs.50 per 80m2 is Rs.25000, find the base and height of the field.

Answer 1

Answer:

Since the cost of cultivating the field at at the rate of Rs. 36.72 per 100 square metre

is Rs. 49,572 => Area of the field =

36.72

49,572×100

=135000sqm

Now, area of the triangular field =

2

1

× base × height =135000

=>

2

1

×(3h)×(h)=135000

=>h

2

=90000

=>h=300m

And base =3×300=900m

Answer 2

Given : The base of a triangular field is twice its height. The cost of cultivating it at the  rate of Rs.50 per 80m² is Rs.25000,

To find  : the base and height of the field.

Solution:

Let say Area of field = A

cost of cultivating  of 80m²   = Rs 50

=> cost of cultivating  of 1 m²   = Rs 50/80

=> cost of cultivating  of 1 m²   =  5/8  Rs

=> cost of cultivating  of A m²   =  A5/8  Rs

A5/8 = 25000

=> A  = 40000 m²

Area of field =  40000 m²

Height = H

Base = 2H

Area = (1/2) Base * height

= (1/2) 2H * H

= H²

H² = 40000

=> H = 200  m

Height = 200 m

Base = 2H = 400 m

base and height of the field are 400 and 200 m respectively

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