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MATH / The 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 long…

Problem

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problem

The 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 aba\sqrt{b} (expressed in simplest radical form), find a+ba+b.
Plain-text mathematical notation (without MathML)
The 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√(b) (expressed in simplest radical form), find a+b.
Original LaTeX notation
The 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 $a+b$.

level

Level 4

type

Geometry

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Source and history

task_id
e21b0fcc-f8e5-58dc-86a0-3dbea70b4443
task_key
geometry--test--e21b0fcc-f8e5-58dc-86a0-3dbea70b4443
task_revision_id
1
config / split
geometry / test

Official source

initial import