Question

A certain 7 sided polygon has sides with 7 different lengths. The first side is the longest. The second side is one unit shorter than the first side. The third side is 3 units shorter than the second. The fourth side is 5 units shorter than the third and so the patterns continues for the other sides. The perimeter of the polygon is 153. Find the length of the longest side. I’ve tried so many different ways of doing this but can’t get a correct answer please help

Answer 1

Just translate each of the sentences to math.
let the longest side be x
2nd side = x - 1
3rd side = x-1 - 3 = x - 4
4th side = x-4 - 5 = x - 9
looks like the "pattern" is to subtract consecutive odd numbers
5th side = x-9 - 7 = x - 16
6th side = x-16 - 9 = x - 25
7th side = x-25 - 11 = x - 36
the other pattern you will note that the sides are
x - (n-1)^2 , were n goes from 1 to 7

anyway, solve
x + x-1 + x-4 + x-9 + x-16 + x-25 + x-36 = 153
7x = 244
x = 34 6/7 , was expecting a whole number
furthermore, the 7th side would be a negative number,

So either my interpretation of subtracting consecutive odd numbers is wrong, there is a typo, or lastly, the question is bogus.