Question

The sides of a scalene triangle are integers in cm If the perimeter of the triangle is 15 cm, then how many such triangles exist?
A. One
B. Two
C. Three
D. Infinitely many

Answer 1

Correct Answer - C
Given that the sides of the scalene triangle are integers in cm and the perimeter of the triangle is 15 cm.
We know that, no two sides are equal in a scalene triangle.
Also, in a triangle, the sum of any two sides is greater than the third side and the difference of any two sides is less than the third side.
As the perimeter of a scalene triangle is 15 cm, the measures of the sides can be (2 cm, 6 cm, 7 cm), (3 cm, 5 cm, 7 cm) and (4 cm, 5 cm, 6 cm).
Hence , choice (c) follows.
Hence, the correct option is (c).