A farmer has four straight pieces of fencing: 1, 2, 3, and 4 yards in length. What is the maximum area he can enclose by connecting the pieces? Assume the land is flat.
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Maximum area enclosed with sides a, b, c, d of a quadrilateral
= √[ (s - a)(s - b)(s - c)(s - d) ] where s = (a + b + c + d) / 2.
Hence maximum area enclosed with pieces of given lengths
= √[ (5 - 1)(5 - 2)(5 - 3)(5 - 4) = √24 = 2√6
= √[ (s - a)(s - b)(s - c)(s - d) ] where s = (a + b + c + d) / 2.
Hence maximum area enclosed with pieces of given lengths
= √[ (5 - 1)(5 - 2)(5 - 3)(5 - 4) = √24 = 2√6
Anonymous:
How do you know that it is maximum?
This is the formula for maximum area with given sides. In this case, opposite angles of the quadrilateral are supplementary.
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