Question 1193613

△{{{ADE}}} ~ △{{{ABC}}}.

<a href="https://imgbb.com/"><img src="https://i.ibb.co/PWrmZSr/triangles.png" alt="triangles" border="0"></a>


Given: {{{DE = 3}}}, {{{AC = 32}}}, {{{EC = BC}}}

if triangles similar, corresponding sides are proportional


{{{BC/DE= AC/EA}}}

{{{EC/DE=AC/AE}}}.....{{{EC=32-AE}}} and {{{DE = 3}}}

{{{(32-AE)/3=32/AE}}}

{{{AE(32-AE)=32*3}}}

{{{32AE-(AE)^2=96}}}

{{{(AE)^2-32AE+96=0}}}

using quadratic formula we have

{{{AE=(-(-32)+-sqrt((-32)^2-4(1)*9))/(2(1))}}}

{{{AE=31.71}}} or {{{0.28}}}=>approximately


{{{EC=32-AE=32-31.71=0.28}}}
or
{{{EC=32-AE=32-0.28=31.72}}}


since {{{EC>AE}}}  , use {{{EC=31.72}}}

then, since {{{BC=EC}}}

 {{{BC=31.72}}}