Question 912169
let's sides be {{{a}}}, {{{b}}}, and {{{c}}} where {{{c}}} is the longest side


One side of triangle,{{{a}}},  is one-third the longest side {{{c}}} => {{{a=(1/3)c}}}


 The third side,{{{b}}}, is {{{7ft}}} less than the longest side {{{c}}} => {{{b=c-7ft}}}

 The perimeter {{{P=77ft}}}. 

solution:

{{{P=77ft}}} .... since {{{P=a+b+c}}} we have 

{{{77ft=a+b+c}}} ......substitute {{{a= (1/3)c}}} and {{{b= c-7ft}}}



{{{77ft=(1/3)c+(c-7ft)+c}}} 

{{{77ft=c/3+c-7ft+c}}} 

{{{77ft+7ft=c/3+2c}}} 

{{{84ft=(c+6c)/3}}} 

{{{3*84ft=c+6c}}} 

{{{252ft=7c}}} 

{{{252ft/7=c}}}

{{{highlight(36ft=c)}}}


now find 
{{{a= (1/3)c}}} and {{{b= c-7ft}}}

{{{a= (1/3)c}}} =>{{{a= (1/3)36ft}}} =>{{{highlight(a= 12ft)}}}

{{{b= c-7ft}}} =>{{{b=36ft-7ft}}} =>{{{highlight(b= 29ft)}}}


check:

 {{{77ft=a+b+c}}} 

{{{77ft=12ft+29ft+36ft}}} 

{{{77ft=77ft}}}