Question 658963
let {{{c}}} be the longest side, {{{a}}} second and {{{b}}} third side

given:

first use this: the third side is {{{12ft}}} less then the longest side


{{{b+12ft=c}}}...........1


then, one side of a triangle is half the longest side:


{{{a=c/2}}}............2


The perimeter is {{{P=53ft}}}, means {{{a+b+c=53ft}}}........3
________________________________


{{{b+12ft=c}}}...........1


{{{a=c/2}}}............2


{{{a+b+c=53ft}}}........3
________________________________solve this system


{{{a+b+c=53ft}}}........3...plug in {{{a=c/2}}} from 2


{{{c/2+b+c=53ft}}}......3a..go to 1 and solve for {{{b}}}



{{{b+12ft=c}}}...........1


{{{b=c-12ft}}}...........plug it in 3a



{{{c/2+(c-12ft)+c=53ft}}}....solve for {{{c}}}


{{{c/2+c-12ft+c=53ft}}}


{{{c/2+2c=53ft+12ft}}}


{{{c/2+2c=65ft}}}........both sides multiply by {{{2}}}


{{{2c/2+2*2c=2*65ft}}}


{{{c+4c=130ft}}}


{{{5c=130ft}}}


{{{c=130ft/5}}}


{{{highlight(c=26ft)}}}


go to {{{b=c-12ft}}} and find {{{b}}}


{{{b=26ft-12ft}}}


{{{highlight(b=14ft)}}}


and finally, go to {{{a=c/2}}}....2 and find {{{a}}}


{{{a=26ft/2}}}


{{{highlight(a=13ft)}}}