Question

the sides of triangular park are 60m 112m and 164m the cost of levelling the park @ rate 8.5 per metre square is​

Answer 1

$\large{\underline{\underline{\mathrm{\red{Answer-}}}}}$

Cost of levelling it at the rate of 8.5 per metre square = Rs. 17136

$\large{\underline{\underline{\mathrm{\red{Explanation-}}}}}$

We've to find the area of ∆ by using heron's formula,

$\huge{\boxed{\rm{S\:=\:\dfrac{a+b+c}{2}}}}$

$\begin{lgathered}\bold{Here} \begin{cases}\sf{S\:refers\:to\:semi\:perimeter} \\ \sf{a\:=\:60\:m}\\ \sf{b\:=\:112\:m} \\ \sf{c\:=\:164\:m}\end{cases}\end{lgathered}$

So let's find semi perimeter first,

$\implies$ S = $\dfrac{60\:+\:112\:+\:164}{2}$

$\implies$ S = $\cancel{\dfrac{336}{2}}$

$\implies$ S = 168 m

Now, herons formula :

$\large{\boxed{\rm{\red{\sqrt{s(s - a)(s - b)(s - c)}}}}}$

Putting the values,

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

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

$\implies$ $\sqrt{4064256}$

$\implies$ 2016 m²

$\therefore$ Area of triangular plot is 2016 m²

Now cost of levelling it at the rate of 8.5 per metre square :

$\implies$ Area of triangular plot × 8.5

$\implies$ 2016 × 8.5

$\implies$ Rs. 17136

Cost of levelling it at the rate of 8.5 per metre square = Rs. 17136

Answer 2

Answer:

$\bold\red{Cost\:of\:levelling}$ = $\bold{Rs.17,136}$

Step-by-step explanation:

$\bf{Given:-}\begin{cases}\sf{a = 60\:m}\\\sf{b = 112\:m}\\\sf{c = 164\:m}\\\sf{Rate = 8.5\:per\:{m}^{2}}\\\sf{Cost\:of\:levelling=?}\end{cases}$

We know that,

$\small{\boxed{\bold\purple{Area\:of\:triangle = \sqrt{s(s-a)(s-b)(s-c)}}}}$

Where, s = half of perimeter of triangle.

$\Rightarrow\sf s =\dfrac{60 + 112 + 164}{2} \\\\\Rightarrow\sf s =\cancel{\dfrac{336}{2}}\:m \\\\\Rightarrow{\boxed{\sf{s = 168\:m}}}$

$\rule{300}{1}$

$\Rightarrow\sf Area =\sqrt{168(168-60)(168-112)(168-164)} \\\\\Rightarrow\sf Area =\sqrt{168 \times 108 \times 56 \times 4} \\\\\Rightarrow\sf Area =\sqrt{4064256}\:{m}^{2} \\\\\Rightarrow{\boxed{\bold\red{Area = 2016\:{m}^{2} }}}$

$\rule{300}{1}$

$\Rightarrow\sf Cost = Area \times Rate \\\\\Rightarrow\sf Cost = Rs.(2016 \times 8.5) \\\\\Rightarrow{\boxed{\bold\red{Cost = Rs.17136}}}$

$\therefore\bold{Cost\:of\:levelling = Rs.17,136}$