Question 525641

let sides be {{{a}}}, {{{b}}} and {{{c}}} where {{{c}}} is the longest side and {{{a}}} is the shortest side

and the perimeter {{{P=a+b+c}}}
given:

the longest side is double the shortest side:
 
{{{c=2a}}}

and the third side is {{{3cm}}} less than the longest side

{{{b+3cm=c}}}........{{{b=c-3cm}}}

 If the perimeter of the triangle is {{{P=57cm}}},than

{{{57cm=a+b+c}}}

{{{57cm=a+(c-3cm)+2a}}}...since {{{c=2a}}}, we have

{{{57cm=a+2a-3cm+2a}}}

{{{57cm+3cm=5a}}}

{{{60cm=5a}}}

{{{60cm/5=a}}}

{{{highlight(12cm=a)}}}....now find {{{b}}} and {{{c}}}

{{{c=2a}}}

{{{c=2*12cm}}}

{{{highlight(c=24cm)}}}

{{{b=c-3cm}}}

{{{b=24cm-3cm}}}

{{{highlight(b=21cm)}}}

check:

{{{57cm=a+b+c}}}

{{{57cm=12cm+21cm+24cm}}}

{{{57cm=57cm}}}