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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 $a+b$.

 Oct 14, 2019
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 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

 

 

 

cool cool cool

 Oct 14, 2019

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