Question

How many scalene triangles with integral sides ( in cm) have a perimeter of 20 cm ?

Answer 1

It is a triangle. So no side could be larger than [Math Processing Error]. If we allow degenerate triangles, we can have flat triangles as (9\cm,8\cm,1\cm)(9\cm,8\cm,1\cm), (9\cm,7\cm,2\cm)(9\cm,7\cm,2\cm), (9\cm,6\cm,3\cm)(9\cm,6\cm,3\cm), (9\cm,5\cm,4\cm)(9\cm,5\cm,4\cm). Otherwise we should exclude them.

The larger side should be either 8\cm8\cm or 7\cm7\cm, as the equilateral triangle of 6\cm6\cmside is not scalene.

Also, no isosceles triangle are allowed, so all the alternatives are:

(8\cm,7\cm,3\cm)(8\cm,7\cm,3\cm), (8\cm,6\cm,4\cm)(8\cm,6\cm,4\cm), (7\cm,6\cm,5\cm)(7\cm,6\cm,5\cm).

So the answer is 3 if we exclude degenerate flat triangles, or 7 if we include them.

Answer 2

Hello mate here is your answer.

3 scalene triangles with integral sides can have perimeter of 20 cm.

Hope it helps you.