Question 780019

let the length of a side of the original triangle be {{{x}}}

{{{Perimeter=3x}}}

So new sides are {{{x+20}}},{{{x+30}}},{{{x+40}}}, and

{{{Perimeter=3x+90}}}

The perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle, or {{{2(3x)= 3x+90}}} and {{{3(3x)=3x+90}}}

So {{{2(3x)<=3x+90<=3(3x)}}}

{{{6x<=3x+90<=9x}}}

{{{3x<=90<=6x}}}

so {{{x<=30}}} and {{{x>=15}}}

So the side lengths of the original triangle are between {{{15cm}}} and {{{30cm}}}, or {{{15cm<=x<=30cm}}}.