Răspuns:
Explicație pas cu pas:
[tex]A_{ABC}=\frac{AC\cdot AB}{2}[/tex]
Notam BD=x ⇒CD=x+2
Aplicam Teorema inaltimii
AD²=BD×CD
80=x(x+2)
x²+2x-80=0
Δ=4+320=324
x=8⇒ BD=8 si CD=10
BC=8+10=18
Aplicam teorema catetei
AB²=BD×BC
AB²=8×18=144
AB=12
AC²=CD×BD=10×18=180
AC=6√5
[tex]A_{ABC}=\frac{6\sqrt{5} \cdot 12}{2}=36\sqrt{5}[/tex]
