[tex]area = l \times w \\ but \: w = l - 2[/tex]
[tex]area = l(l - 2) = l {}^{2} - 2l[/tex]
[tex]l {}^{2} - 2l \geqslant 48 \\ l {}^{2} - 2l - 48 \geqslant 0 \\ (l + 6)(l - 8) \geqslant 0[/tex]
[tex]l {}^{2} - 2l \leqslant 80 \\ l {}^{2} - 2l - 80 \leqslant 0 \\ (l + 8)(l - 10) \leqslant 0[/tex]
Sol 1: L in ]-∞,-6]U[8,∞[
Sol 2: L in [-8,10]
Intersection:
L belongs [-8,-6[U[8,10]
But Length cannot be negative
L belongs [8,10] or 8≤L≤10
