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The area of the triangular field is found by using here’s formula i.e.

\[\sqrt {S(s - a)(s - b)(s - c)} \] where a, b, c are sides of the triangle

S is semi perimeter.

Value of \[s = \dfrac{{a + b + c}}{2}\]

Therefore

Given sides of triangular grass field \[50n,65m\]and \[65m\] respectively

Let \[a = 50m\]

\[b = 65m\]

and \[c = 65m\]

Now \[S = \dfrac{{a + b + c}}{2} = \dfrac{{50 + 65 + 65}}{2} = 90m\]

Area of triangular field is found by heron’s formula

i.e. Area \[ = \sqrt {S(s - a)(s - b)(s - c)} \]

put \[s = 90m,a = 50m,b = 65m\] and \[c = 65m\]

Area \[ = \left[ {{{10}^2} \times {3^2} \times {2^2} \times {{25}^2}} \right]\]

\[ = \sqrt {90(40)(25)(25)} \]

\[ = \sqrt {10 \times 910 \times 4 \times 25 \times 25} \] \[\left[ {\because 90 = 9 \times 10\,\,40 = 4 \times 10} \right]\]

\[ = \left[ {{{10}^2} \times {3^2} \times {2^2} \times {{25}^2}} \right]\] \[\left[ {\because {3^2} = 9\,4 = {2^2}} \right]\]

\[ = 10 \times 3 \times 2 \times 25\]

Area\[ = 1500{m^2}\]

BY unitary method,

Cost of laying \[I{m^2}\] grass \[ = Rs.7\](Given)

Cost of laying \[1500{m^2}\] grass

\[ = Rs\,1500 \times 7 = Rs\,10500\]

Hence the cost of laying is Rs. \[1050\].