Question

triunghiul ABC isoscel ori(AB)=(AC);m(∆A)=120°;BC=36cm.Se cere Perimetrul triunghiului ABC=?;aria=?

Answer 1

triunghi isoscel  ⇒ inaltime AD si mediana   ⇒BD=DC=36/2=18 cm
m(∡CAD)=m(∡BAD)=120°/2=60°
m(∡ACD)=90°-m(∡CAD)=90°-60°=30°
teorema unghiului de 30° ⇒ AC=2AD
notam AD=x     AC=2x
AC²-AD²=DC²
(2x)²-x²=18²
4x²-x²=324
3x²=324
x²=324:3=108
x=√108=6√3 cm  ⇒ AC=AB=2×6√3=12√3
P=2×12√3+36=24√3+36=12(2√3+3) cm
A=BC×AD/2=36×6√3/2=108√3 cm²