Question

Dau coroana!Imi trebuie urgent. Va rog frumos ajutati-ma.Doar b si c.
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Answer 1

 

$\displaystyle\\\text{Calculam aria }~\Delta ABC \text{ cu formula lui Heron.}\\\\\text{Perimetrul}~~P=AB+AC+BC=13+14+15=42~m\\\\\text{Semiperimetrul}~~p=\frac{P}{2}=\frac{42}{2}=21~m\\\\A_{\Delta ABC}=\sqrt{p(p-AB)(p-AC)(p-BC)}=\\\\=\sqrt{21(21-13)(21-14)(21-15)}=\\\\=\sqrt{21\times8\times7\times6}=\\\\=\sqrt{3\cdot7\times2^3\times7\times3\cdot2}=\\\\=\sqrt{3^2\cdot7^2\times2^4}=\\\\=3\times7\times2^2=21\times4=\boxed{\bf84~m^2}~~\text{(Aria triunghiului ABC)}$

$\displaystyle\\\text{Calculam raza cercului circumscris cu formula:}\\\\A_{\Delta ABC}=\frac{AB\times AC\times BC}{4R}\\\\ \text{in care R este necunoscuta.}\\\\R=\frac{AB\times AC\times BC}{4A}=\\\\=\frac{13\times14\times15}{4\times84}=\frac{13\times15}{4\times6}=\frac{13\times5}{4\times2}=\frac{65}{8}=8,\!125~m\\\\\text{Calculam aria cercului:}\\\\A\circ=\pi R^2=3,15\times 8,\!125^2\\\\8,\!125^2=66,015625 \approx 66\\\\A\circ=3,15\times 66=207,9 \approx \boxed{\bf208~m^2}$

$\displaystyle\\a)~\text{Suprafata parcului este aria cercului calculata mai sus.}\\\boxed{\bf A\circ \approx 208~m^2}\\\\b)~\text{Suprafata locului de joaca este aria triunghiului calculata mai sus.}\\\boxed{\bf A_{\Delta ABC}=84~m^2}\\\\c)\\\text{Intre triunghi si conturul cercului se planteaza gazon.}\\\\\text{Aria zonei cu gazon o calculam cu formula:}\\\\ A_G = A\circ-A_{\Delta ABC}=208-84=\boxed{\bf124~m^2}\\\\\text{Sunt necesare seminte de gazon in cantitate de}~40~g/m^2$

$\displaystyle\\\\\text{Pentru }~124~m^2~\text{ de gazon sunt necesare:}\\\\ 124\times 40 = 4960~g = \boxed{\bf4,\!960~Kg~de~seminte}\approx \boxed{\bf5~Kg~de~seminte}$