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Find the area of a triangular field, th...

Find the area of a triangular field, the length of whose sides are 275 m, 660 m and 715 m. What is the cost of cultivating the field at the rate of Rs. 200 per hectare ?

Text Solution

Verified by Experts

Let a = 275 m, b = 660 m and c = 715 m
`:. S=(1)/(2)(a+b+c)=(1)/(2) (275+660+715)=825 m`
Area of the triangle given by
`Delta = sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(825(825-275)(825-660)(825-715))`
`=sqrt(825xx550xx165xx110)`
`=sqrt(5^(2)xx3xx11xx5^(2)xx2xx11xx3xx5xx11xx2xx5xx11)`
`=5^(2)xx3xx11^(2)xx2=90750 m^(2)`
Thus, area of field = `90750 m^(2)`
Now, the cost of cultivating 10000`m^(2)` = Rs. 200
`:.` The cost of cultivating the given field
`Rs. ((200)/(10000)xx90750)=Rs. 1815.0`
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