The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length 1 cm, 2 cm and 4 cm, then the total number of possible lengths of the fourth side is
Explanation:
In a quadrilateral, the longest side is less than the sum of other three sides and greater than the least of the difference of any 2 of the other three sides.
Let the fourthe sides of the quadrilateral be x.
⇒ 2 - 1 < x < 1 + 2 + 4 ⇒ 1 < x < 7 ∴ x can be 2, 3, 4, 5 or 6
Hence, x can take 5 integral values.
Hence, option (a).
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