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GeoGebraGeoGebra Classroom

Rectangle Perimeter Given Area

The area of the rectangle is fixed. Drag point X to change the rectangle's dimensions.
1) Set the area of the rectange to 36 using the slider. Make a prediction for the dimensions of the perimeter that have the longest perimeter and the shortest perimeter. (Dimensions should be whole numbers.) 2) Drag the point X to change the rectangle's dimensions. Record the length, width, perimeter and area for the rectangles. Compare your data with your predictions. Which rectangle has the longest perimeter? Which had the shortest perimeter? 3) Use the slider to explore rectangles of different area. Make a conjecture for any given area of a rectangle, what will be the dimensions of the rectangle with the longest perimeter? What about the shortest perimeter?