Question

Problema urmàtoare 3

Answer 1

Răspuns:

Explicație pas cu pas:

$A_{ABC}=\frac{AC\cdot AB}{2}$

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

$A_{ABC}=\frac{6\sqrt{5} \cdot 12}{2}=36\sqrt{5}$