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Rectangles: Perimeter v. Area

Directions: How can you tell which rectangle is bigger: a rectangle with a perimeter of 24 units or a rectangle with an area of 24 square units?



What does “bigger” mean?  What information to we need to compare these two squares?



I have intentionally left the word “bigger” mathematically imprecise.  Depending on whether “bigger” refers to a greater area or greater perimeter, you will get different answers.  For example, a let’s assume that the rectangle with an area of 24 square units measures 6 units by 4 units.  Now let’s consider two different rectangles with perimeters of 24 units.  Rectangle A is 6 units by 6 units.  That has an area of 36 square units and has a bigger area than the initial rectangle.  Rectangle B is 11 units by 1 unit.  That has an area of 11 square units and has a smaller area than the initial rectangle.  Hopefully this will provide good opportunities to develop the need for precise mathematical language.

Source: Robert Kaplinsky

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  1. Hi, Robert! Minor thing here, but I think the hint should say “rectangles” and not “squares”…? Students could use any sort of rectangle to consider this problem, right?

  2. Isabella Mendoza

    i think the answer is the perimeter of 24 units because then the area is going to be bigger than 24 units.

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