[tex]\displaystyle\\\text{Se da un triunghi cu laturile:}\\17m, 10m\text{ si }21m\\\\Se cere:\\\text{Aria triunghiului.}\\\\\text{Rezolvare:}\\\\\text{Folosim formula lui Heron.}\\\\A=\sqrt{p(p-a)(p-b)(p-c)}\\\\\text{unde }~a,b,c~\text{ sunt lungimile laturilor}\\\\\text{si}~p=\frac{a+b+c}{2}=\text{semiperimetrul}[/tex]
[tex]\displaystyle\\\text{Calcule:}\\\\P=17+10+21=48~m\\\\p=\frac{P}{2}=\frac{48}{2}=24~m\\\\A=\sqrt{24(24-17)(24-10)(24-21)}\\\\A=\sqrt{24\times7\times14\times3}\\\\A=\sqrt{(8\times3)\times7\times(7\times 2)\times3}\\\\A=\sqrt{(8\times2)\times(7\times7)\times(3\times3)}\\\\A=\sqrt{16\times49\times9}\\\\A=4\times7\times3\\\\\boxed{\bf A=84~m^2}\\\\\text{Raspuns corect: }~ \boxed{\bf d)~84m^2}[/tex]
