Question

The perimeter of a scalene triangle is 8 units and the lengths of its sides are integers, then the number of such possible triangle is

• A. 0
• B. 2
• C. 1
• D. 4

Answer 1

The correct option is A 0

In a scalene triangle, the lengths of all sides are unequal.
Since the lengths of its sides should be integers.
Therefore, the possible lengths of triangle when its perimeter is 8 units can be 1 unit, 4 units and 3 units or, 1 unit, 2 unit and 5 unit.
Consider the triangle with dimensions 1 units, 4 units and 3 units
Here, 4 – 3 = 1
Since the difference of any two sides of a triangle should be less than the third side, thus this triangle cannot be constructed.
Now, consider the triangle with dimensions 1 unit, 2 units and 5 units.
Here, 1 + 2 = 3 < 5
Since the sum of any two sides of a triangle should be greater than the third side, thus this triangle too cannot be constructed.
Therefore, no triangle is possible with the given conditions.
Hence, the correct answer is option (a).