Design an optimal rectangular school garden with integer outer side lengths given a fixed outer perimeter and a fixed-width internal walkway around the planting bed; determine the outer dimensions that maximize the plantable area (inner rectangle), compute outer and inner areas and perimeters, calculate the percent of total space devoted to planting versus paths, and provide a clear diagram plus step-by-step calculations and a justification comparing reasonable integer alternatives to show why your chosen dimensions are optimal. This assesses geometry (area/perimeter), integer reasoning, percentages, and problem-solving for Grade 6–8 advanced students.