Use coordinate methods to compute polygon perimeters and areas of triangles/rectangles.
Find a missing coordinate from rectangle area
Problem
An axis-aligned rectangle has consecutive vertices \((0,0)\), \((x,0)\), \((x,4)\), \((0,4)\) and area \(28\), with no assumed left-right order. Derive the width, write the absolute-value equation, solve for all real \(x\)-values, and check them.
Use the area and known height to determine the rectangle’s positive missing width. That width is an absolute coordinate difference from the fixed endpoint, so solve the resulting distance relationship in both directions and retain both locations when no left-or-right restriction is given.
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