Question

Care este aria unui triunghi cu lg de laturilor de 13,14 si 15 cm?

Answer 1

Aplicăm formula lui Heron :

[tex]\it \mathcal{A} = \sqrt{p(p-a)(p-b)(p-c)} \\\;\\ \\\;\\ p = \dfrac{13+14+15}{2} = 42\2=21 \\\;\\ \\\;\\ 21-13 = 8, \ \ 21 - 14 = 7,\ \ 21 - 15 = 6[/tex]


$\it \mathcal{A} = \sqrt{21\cdot8\cdot7\cdot6} = \sqrt{3\cdot7\cdot4\cdot2\cdot7\cdot6} = \sqrt{36\cdot49\cdot4} = 6\cdot7\cdot2=84$cm²

Answer 2

$\boxed{Formula \ lui \ Heron : \sqrt{p(p-a)(p-b)(p-c)} } \\ \\ \it Semiperimetrul : \ p= \dfrac{P}{2} \\ \\ p= \dfrac{13+14+15}{2} \\ \\ p= \dfrac{42}{2} \\ \\ p=21 \ cm \\ \\ A= \sqrt{p(p-a)(p-b)(p-c)} \\ \\ A = \sqrt{21(21-13)(21-14)(21-15)} \\ \\ A= \sqrt{21 \times 8 \times 7 \times 6 } \\ \\ A = \sqrt{7 \times 3 \times 2^3 \times 7 \times 2 \times 3} \\ \\ A = \sqrt{7^2 \times 3^2 \times 2^4} \\ \\ A = 7 \times 3 \times 2^2 \\ \\ A = 21 \times 4 \\ \\ \boxed{A = 84 \ cm^2}$