For any positive integer $n \geq 2$, let $T_{n}$ denote a triangle with side lengths $n, n+1, n+2$. Select the correct options. (Note: If a triangle has side lengths $a, b, c$ respectively, let $s = \frac{a+b+c}{2}$, then the area of the triangle is $\sqrt{s(s-a)(s-b)(s-c)}$) (1) $T_{n}$ is always an acute triangle (2) The perimeters of $T_{2}, T_{3}, T_{4}, \cdots, T_{10}$ form an arithmetic sequence (3) The area of $T_{n}$ increases as $n$ increases (4) The three altitudes of $T_{5}$ form an arithmetic sequence in order (5) The largest angle of $T_{3}$ is greater than the largest angle of $T_{2}$
For any positive integer $n \geq 2$, let $T_{n}$ denote a triangle with side lengths $n, n+1, n+2$. Select the correct options.\\
(Note: If a triangle has side lengths $a, b, c$ respectively, let $s = \frac{a+b+c}{2}$, then the area of the triangle is $\sqrt{s(s-a)(s-b)(s-c)}$)\\
(1) $T_{n}$ is always an acute triangle\\
(2) The perimeters of $T_{2}, T_{3}, T_{4}, \cdots, T_{10}$ form an arithmetic sequence\\
(3) The area of $T_{n}$ increases as $n$ increases\\
(4) The three altitudes of $T_{5}$ form an arithmetic sequence in order\\
(5) The largest angle of $T_{3}$ is greater than the largest angle of $T_{2}$