Question

ABCD este un triunghi cu AB=24cm, AC=28cm si BC=32 cm .Aflati raza cercului inscris in trunghi​

Answer 1

Răspuns:

Explicație pas cu pas:

$\texttt{Vom calcula aria triunghiulu prin formula lui Heron.}\\P=AB+AC+BC\\P=24+28+32=84~cm\\p=\dfrac{P}{2}=42~cm\\A=\sqrt{p(p-AB)(p-AC)(p-BC)}\\A=\sqrt{42(42-24)(42-32)(42-28)}\\A=\sqrt{42\cdot 18\cdot 10\cdot 14}\\A=\sqrt{14^2\cdot3^2\cdot 2^2\cdot 15}\\A=14\cdot 3\cdot 2\sqrt{15}\\A=84\sqrt{15}~cm^2\\r=\dfrac{A}{p}\\r=\dfrac{84\sqrt{15}}{42}=2\sqrt{15}\\\boxed{r=2\sqrt{15}~cm}$