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 &nbsp;

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Question :

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

Started 1 month ago by Shashank in

0 61

A.
6
B.
4
C.
5
D.
3

Option C is the correct answer.

Explanatory Answer

In any polygon, the largest side length should be less than the sum of the lengths of the other sides.
Let the fourth side be ‘x’.
Case i) x is the largest side.
x < 1 + 2 + 6
x < 7
x can take the following values, 4, 5, 6
Case ii)
4 is the largest side and x is less than 4.
4 < x + 1 +2
x > 1
x can take the values 2 or 3
So, x can take the values 2, 3, 4, 5, 6.
x can take 5 values.