The set of all solutions of the system

is a quadrilateral region. Find the number of units in the length of the longest side. Express your answer in simplest radical form.

Guest Mar 10, 2019

#1**+1 **

We can use a graph to help with this : https://www.desmos.com/calculator/4beobd4b3x

The vertex points of the quadrilateral are (0, 3) (0,2) (1,0) and (3, 0)

By visual inspection , the longest side is the distance from (0,3) to (3,0)

And this distance = √ [ (3 - 0)^2 + (3 - 0)^2 ] = √ [9 + 9 ] = √18 = 3√2 units

CPhill Mar 11, 2019