Răspuns:
12
Explicație pas cu pas:
[tex]\ell_{n} = \ell_{1} + (n - 1)\cdot r \\ 38 = \ell_{1} + (n - 1)\cdot 3 \\ \implies \ell_{1} = 41 - 3n[/tex]
[tex]P_{n} = \frac{(\ell_{1} + \ell_{n})\cdot n}{2} \\258 = \frac{(41 - 3n + 38)\cdot n}{2} \\ 516 = 79n - 3 {n}^{2} \\ 3 {n}^{2} - 79n + 516 = 0 \\ (3n - 43)(n - 12) = 0[/tex]
[tex]n_{1} = \frac{43}{3} \not \in \mathbb{N} \\ n_{2} = 12 \in \mathbb{N}[/tex]
=> poligonul are 12 laturi
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Verified answer
Răspuns:
12
Explicație pas cu pas:
[tex]\ell_{n} = \ell_{1} + (n - 1)\cdot r \\ 38 = \ell_{1} + (n - 1)\cdot 3 \\ \implies \ell_{1} = 41 - 3n[/tex]
[tex]P_{n} = \frac{(\ell_{1} + \ell_{n})\cdot n}{2} \\258 = \frac{(41 - 3n + 38)\cdot n}{2} \\ 516 = 79n - 3 {n}^{2} \\ 3 {n}^{2} - 79n + 516 = 0 \\ (3n - 43)(n - 12) = 0[/tex]
[tex]n_{1} = \frac{43}{3} \not \in \mathbb{N} \\ n_{2} = 12 \in \mathbb{N}[/tex]
=> poligonul are 12 laturi