Question Number 12074 by sin (x) last updated on 11/Apr/17
Answered by ajfour last updated on 11/Apr/17
Commented by ajfour last updated on 11/Apr/17
$${M}\:{is}\:{the}\:{mid}-{point}\:{of}\:{CD}. \\ $$$${let}\:{side}\:{of}\:{triangle}\:{be}\:\:\boldsymbol{{a}}\:. \\ $$$$\boldsymbol{\mathrm{BM}}=\boldsymbol{\mathrm{BC}}−\boldsymbol{\mathrm{CM}} \\ $$$$\:\:\:\:\:\:\:\:=\boldsymbol{\mathrm{a}}−\frac{\boldsymbol{\mathrm{a}}+\mathrm{8}}{\mathrm{2}}=\frac{\boldsymbol{\mathrm{a}}−\mathrm{8}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{BE}}=\boldsymbol{\mathrm{BM}}/\mathrm{cos}\:\mathrm{60}\:=\:\boldsymbol{\mathrm{a}}−\mathrm{8} \\ $$$$\boldsymbol{\mathrm{AB}}=\:\boldsymbol{\mathrm{a}} \\ $$$$\boldsymbol{\mathrm{AE}}\:=\:\boldsymbol{\mathrm{AB}}−\boldsymbol{\mathrm{BE}}\:=\boldsymbol{\mathrm{a}}−\left(\boldsymbol{\mathrm{a}}−\mathrm{8}\right)=\mathrm{8cm}. \\ $$