he set of all solutions of the system\[ \begin{cases}& 2x+y \le 4 \\& x+y \ge 1 \\& x \ge 0 \\& y \ge 0 \end{cases} \]is a quadrilateral region. If the number of units in the length of the longest side is $a\sqrt{b}$ (expressed in simplest radical form), find $a+b$.
+128473 2x+y ≤ 4 , x+y ≥1 , x ≥ 0 , y ≥ 0
See the following graph : https://www.desmos.com/calculator/otkx3figgt
The longest side connects the vertices (0,4) and (2,0)
The length of the longest side is sqrt [ (2 - 0)^2 + (4 - 0)^2] = sqrt [ 4 + 16] = sqrt (20) = 2sqrt(5)
So a = 2 and b = 5
a + b = 7
