The triangular side walls of a flyover have been used for advertisements. The sides of the walls are `13m, 14m` and `15m.` The advertisements yield an earning of rupee `2000` per `m^(2)` a year. A company hired one of its walls for `6` months. How much rent did it pay?

Explanation

Since, the sides of triangular walls are `a =13 m, b=14 m` and `c=15 m`
`therefore" semi-perimeter of a triangular side wall, "s=(a+b+c)/(2)=(13+14+15)/(2)=(42)/(2)=21m`
`therefore" Area of triangular side wall"=sqrt(s(s-a)(s-b)(s-c))" "["by Heron's formula"]`
`=sqrt(21(21-13)(21-14)(21-15))`
`=sqrt(21xx8xx7xx6)`
`=sqrt(21xx4xx2xx7xx3xx2)`
`=sqrt((21)^(2)xx(4)^(2))=21xx4=84m^(2)`
Since, the advertisement yield eaming per year for 1 `m^(2)`= rupee 2000
`therefore"Advertisement yield earning per year on "84 m^(2)=2000xx84="rupee " 168000`
As the company hired one of its walls for 6 months, therefore company pay the rent `=(1)/(2)(168000)="rupee " 84000`
Hence, the company paid rent rupee `84000.`