Question

how many Triangles are there with perimeter of 24cm and integral sides ??

Please help
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Answer 1

Answer:

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

Step-by-step explanation:

there are eight triangles

hope it's helpful