The sides of a triangular park are 60 m, 112 m and 164 m.The cost of levelling the park at the rate of ₹8.50/m$$^2$$ is:

Let the side of Triangular part be  a= 60 m, b= 112 m, c=164m 

then S= $$\dfrac{a+b+c}{2} =\dfrac{60+112+164}{2}$$

$$\Rightarrow s=168 $$

Area of Trinagle = $$ \sqrt{s(s-a)(s-b)(s-c)} $$ 

$$\Rightarrow \sqrt{168(168-60)(168-112)(168-164)}$$

$$\Rightarrow \sqrt{168(108)(56)(4)}$$

$$\Rightarrow \sqrt{2^3 \times 7 \times 3 \times 2^2  \times 3^3 \times 2^3 \times 7 \times 2^2}$$

$$\Rightarrow \sqrt{2^10 \times 7^2 \times 3^4}$$

$$\Rightarrow 2^5 \times 7 \times 3^2 $$

$$\Rightarrow 2016  m^2 $$

Now the cost of levelling the park = $$ 2016 \times 8.50 $$

$$\Rightarrow Rs  17136 $$ Ans