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

Question

Accepted Answer

### Key Concept: 
For any polygon (in this case, a quadrilateral), the largest side must be less than the sum of the other three sides. In this case, the fourth side is denoted as $x$.

### Case 1: $x$ is the largest side.
If $x$ is the largest side, then the inequality can be written as:

x < 1 + 2 + 4 = 7.

So, $x$ can take values less than 7. Therefore, $x$ could be:

x = 4, 5, 6.

### Case 2: 4 is the largest side, and $x$ is smaller than 4.
Here, the inequality becomes:

x + 1 + 2 > 4

which simplifies to:

x > 1.

Thus, $x$ can take values greater than 1 and less than 4, so $x$ could be:

x = 2, 3.

### Combine Both Cases:
From Case 1 and Case 2, the possible values for $x$ are:

x = {2, 3, 4, 5, 6}.

### Conclusion:
The total number of possible values for $x$ is 5. Therefore, the correct answer is **C**.

Answer

Answer

Answer