Find the cost of laying grass in a triangular field of sides `50 m, 65 m` and `65 m` at the rate of rupee `7` per `m^(2)`.

Explanation

Since, `ABC` is a triangular field of sides
`AB=a=50 m, BC=b=65 m` and `CA=c=65m.`

`therefore"Semi-perimeter of triangular field,"`
`s=(a+b+c)/(2)=(50+65+65)/(2)=(180)/(2)`
`therefore"Area of a triangular field"`
`=sqrt(s(s-a)(s-b)(s-c))" "["by Heron's formula"]`
`=sqrt(90(90-50)(90-65)(90-65))`
`=sqrt(90xx40xx25xx25)`
`=3xx2xx10xx25`
`=6xx250=1500 m^(2)`
`because"Cost of laying grass per "1m^(2)="rupee "7`
`because"Cost of laying grass per "1500m^(2)=7xx1500="rupee "10500`
`"Hence, the cost of laying grass in a triangular field is " "rupee "10500.`