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[[1]] is the cost of laying grass in a triangular field of sides 50m,65m and 65m at the rate of Rs 7 per m2.

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Detailed Solution

Given sides of triangular, let a = 50m, b= 65m and c= 65m
Now

S = \frac{a + b + c}{2} = \frac{50 + 65 + 65}{2} = 90 mArea 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 = [10^{2} \times 3^{2} \times 2^{2} \times 25^{2}]

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

= \sqrt{10 \times 910 \times 4 \times 25 \times 25}

[∵90=9×10 40=4×10]

= [10^{2} \times 3^{2} \times 2^{2} \times 25^{2}

]

[∵ 3^{2} = 9 4 = 2^{2}]

=10×3×2×25
Area =1500m2
By unitary method,
Cost of laying 1m2 grass =Rs.7(Given)
Cost of laying 1500m2 grass=Rs1500×7=Rs1050
Hence the cost of laying is Rs.10500

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