The lengths of the sides of a triangle are consecutive odd integers. if the perimeter of the triangle is 27 what is are the lengths of all three sides?

Bearing in mind that, if you multiply any integer whatsoever, by 2, you get an even number, 3*2 or 17*2 or 4*2 and so on.

to get an ODD integer, simply hop once forward of backwards from any even integer, 2-1, or 2+1 or  8+1 or 8-1.

to get a consecutive ODD integer, simply hop twice from any odd integer, say 3+2, or 7+2 and so on.

now, let's pick a reference integer, say hmmm "a".

we know that a * 2, or 2a is an even integer, therefore (2a + 1) is an ODD integer, and (2a +1 ) + 2 is a consecutive odd integer.  So, there you have it, our first two odd integers, and the next one, is, you guessed it, (2a + 1) + 2 + 2

so, our three odd consecutive integers are (2a+1), (2a+3) and (2a+5)

so, the triangle has a perimeter of 27, so, let's add them up then



so, our first odd integer is

2a + 1

2(3) + 1 --> 7

and surely you know what the other two are.

Ithink it would be 160 people