Question

the altitude and the base of a triangular field are in the ratio 6:5. If its cost is ₹ 49,57,200at the rate of ₹ 36,720 per hectare and 1 hectare is 10,000 sq. m, find dimensions of the field ( in metre)

Answer 1

let the altitude of field be h and base be b

Thus          h:b = 6:5
                    h= 6/5 b
area of field = 1/2 b*h
 in hectares, area of field  = (1/10000)*1/2*bh

According to question
Cost of 1 hectare = 36,720 rupees

and total cost is 49,57,200 rupees
Thus, 

                Total cost = cost of 1 hectare * total area
                 49,57,200= 36.720 * (1/20000) bh

putting  h = 6/5b
         
                 49,57,200 = 36,720 * (1/20000) 6/5b^2
                               b^2 = 123.456
                                 b= 11.11 m
                         thus h= 6/5 * 11.11
                                 h = 1.2*11.11
                                 h = 13.332 m