The cost of ploughing the rectangular field at the rate of Rs.100 per square meter is Rs.49300.If the perimeter of the field is 92m, find the length and breadth of the field
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Area = l × b = 49300/100
lb = 493
Perimeter = 2 (l + b) = 92
l + b = 46
(l - b) {}^{2} = (l + b) {}^{2} - 4lb(l−b)
2
=(l+b)
2
−4lb
(l - b) {}^{2} = 46 {}^{2} - 4 \times 493(l−b)
2
=46
2
−4×493
(l - b) {}^{2} = 2116 - 1972(l−b)
2
=2116−1972
(l - b) {}^{2} = 144(l−b)
2
=144
l - b = \sqrt{144}l−b=
144
l-b = 12
\begin{lgathered}l + b = 46 \\ l - b = 12 \\\end{lgathered}
l+b=46
l−b=12
2l = 58
l= 58/2 = 29 m
l + b = 46
b = 46 - 29 = 17 m
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