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The set of all solutions of the system \(\begin{cases} x+y\leq 3 \\ 2x+y\geq 2 \\ x\geq 0 \\ y\geq 0 \end{cases}\) is a quadrilateral region. Find the number of units in the length of the longest side. Express your answer in simplest radical form.

 Mar 9, 2018
 #1
avatar+101870 
+2

Here's a pic of the feasible region :

 

 

The vertices  of the quadrilateral are shown

The longest side =

√ [ 3^2 + 3^2 ]   =

√18 =

3√2   units

 

 

cool cool cool

 Mar 9, 2018
 #2
avatar+4296 
+3

Amazing solution, CPhill! Thanks so much!

tertre  Mar 10, 2018

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