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Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs 7 per m^{2}.

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#### Solution

**Given:** The sides of the ground are a = 50 m, b = 65 m and c = 65 m. Now, the semi-parameter(s) of the cost of levelling is:

2s = a + b + c

2s = 50 m + 65 m + 65 m

2s = 180 m

s = `(180m)/2`

x = 90 m

Area of triangle = `sqrt(s(s - a)(s - b)(s - c))`

= `sqrt(90(90 - 50)(90 - 65)(90 - 65))`

= `sqrt(90 xx 40 xx 25 xx 25)`

= `3 xx 2 xx 10 xx 25`

= `6 xx 250`

= 1500 m^{2}.

The cost of laying grass 1 m^{2} area is Rs. 7

Therefore, the cost of levellng grass per 1500 m^{2} = Rs. 7 × 1500 = Rs. 10500

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