Question

How many scalene triangles of perimeter 20 cm exist, such that the lengths (in cm) of all the three sides are integers?

Answer 1

Answer:

4 combinations.

Step-by-step explanation:

Sum of 2 sides of a triangle is greater than the 3rd side.

In scalene triangle all side are unequal and hence 9 has to be the longest side.

Possible combinations with 9 as the largest side are 3:

1)9, 8, 3

2)9, 7, 4

3)9, 6, 5

If 8 is taken as longest side, possible combinations is:

1)8, 7, 5

Combinations with 7, 6, 5.... are not possible for scalene type of triangle.

So the possible combinations are:

1)9, 8, 3

2)9, 7, 3

3)9, 6, 5

4)8, 7, 5

Hope it helped.