Question 734301

length {{{AB}}}: {{{x + 1cm}}}
length {{{BC}}}: {{{xcm}}}
length {{{AC}}}: {{{sqrt(x^2 + (x+1)^2)cm}}}

It follows that: given perimeter {{{70cm}}}, then

{{{x + (x+1) + sqrt(2*x^2 + 2x + 1) = 70}}}

{{{69 - 2x = sqrt(2*x^2 + 2x + 1)}}}

{{{4x^2 -276x + 69^2 = 2x^2 + 2x + 1}}}

{{{2x^2 - 278x + 4760 = 0}}}...factor

{{{(x-119)(x-20) = 0}}}

solutions:

If {{{(x-119)=0}}}, then {{{x = 119}}}, and it is not a solution for {{{x + (x+1) + sqrt(2*x^2 + 2x + 1) = 70}}} because {{{ x}}} must be less than {{{P=70 cm}}}.

If {{{(x-20)=0}}}, then {{{x = 20}}}.
 
Hence, {{{x = 20 cm}}}.

so,

length {{{BC}}}: {{{20cm}}}
length {{{AB}}}: {{{21cm}}}
length {{{AC}}}: {{{29cm}}}