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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 ?

A

`"Rs. 1800"`

B

`"Rs. 1678"`

C

`"Rs. 1675"`

D

`"Rs. 1815"`

Text Solution

Verified by Experts

The correct Answer is:
D
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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