Explicație pas cu pas:
Ducem inaltimea BD, BD⊥AC
sin75°=BD/BC
(√6+√2)/4=BD/16
BD=16(√6+√2)/4
BD=4(√6+√2)cm
ctg45°=BD/AD⇒1=4(√6+√2)/AD⇒AD=4(√6+√2) cm
AB=√[2*16(√6+√2)²]=4√2*(√6+√2)=(8√3+8) cm
CD=√(16²-16(√6+√2)²)=√[256-16(8+4√3)]=√[256-128-64√3)=√(128-64√3)=
=√[64(2-√3)=8*(√6-√2)/2=(4√6-4√2)cm
AC=AD+CD=4√6+4√2+4√6-4√2=8√6(cm)
P=AB+BC+AC=8√3+8+16+8√6=(24+8√3+8√6) cm
Bafta!!