Question 106390
The consecutive whole numbers can be called 
{{{n}}},{{{n+1}}},{{{n+2}}}
The sum of the 2 longer pieces is {{{2x}}}
What if each longer piece were 100 cm? Then ther would be nothing left for the 
other three pieces
{{{n + (n+1) + (n+2) + 2*100 = 200}}}
Now keep making x smaller and see how much is left for the other three
lengths, and if they can be consecutive numbers.
{{{2x = 198}}}
{{{1+2+3 = 6}}} and {{{6 + 198}}} is too big
{{{2x = 196}}}
{{{1+2+3 = 6}}} is still too big
{{{2x = 194}}}
{{{1+2+3 = 6}}} works out good
{{{194 + 6 = 200}}}
{{{2x = 194}}}
{{{x = 97}}}
So, the lengths are 1,2,3,97,97