[tex]\it \mathcal{A}=\sqrt{p(p-a)(p-b)(p-c)}\ \ Formula\ lui\ Heron\\ \\\\ p=\dfrac{13+14+15}{2}=21 \\ \\ 21-13=8,\ 21-14=7,\ 21-15=6 \\ \\ \\ \mathcal{A}=\sqrt{21\cdot8\cdot7\cdot6}=\sqrt{3\cdot7\cdot4\cdot2\cdot7\cdot6}=\sqrt{2^2\cdot7^2\cdot6^2}=2\cdot7\cdot6=84cm^2[/tex]
Cea mai mică înălțime corespunde laturii cu lungimea cea mai mare.
[tex]\it \mathcal{A}=\dfrac{b\cdot h}{2}\\ \\ \\ \mathcal{A}=\dfrac{15\cdot h}{2} \Rightarrow 84=\dfrac{15\cdot h}{2} \Rightarrow h=84\cdot\dfrac{2}{15}=\dfrac{168^{(3}}{15}=\dfrac{^{2)}56}{\ 5}=\dfrac{112}{10}=11,2cm[/tex]
