Question 1205954


 
let the shortest side be {{{a}}}, the longest side {{{c}}}, and the third side{{{ b }}}

if the shortest side is {{{3 }}}meters less than the longest side we have

{{{a=c-3}}}....eq.1
 

if the length of the third side is {{{11}}} meters less than {{{twice}}} the length of the longest side, we have

{{{b=2c-11}}}....eq.2


 If the perimeter is {{{22}}} meters, we have

{{{a+b+c=22}}}....eq.3


substitute {{{a}}} and{{{ b}}}

{{{c-3+2c-11+c=22}}}....eq.3, solve for {{{c}}}

{{{4c-14=22}}}

{{{4c=22+14}}}

{{{4c=36}}}

{{{c=36/4}}}

{{{c=9}}}


go to

{{{a=c-3}}}....eq.1, substitute {{{c}}}

{{{a=9-3}}}

{{{a=6}}}


go to

{{{b=2c-11}}}....eq.2, substitute {{{c}}}

{{{b=2*9-11}}}

{{{b=18-11}}}

{{{b=7}}}

 the lengths of the three sides of the triangle are: {{{6m}}}, {{{7m}}}, and{{{ 9m}}}