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Rectangles: Maximizing Perimeter

Directions: What is the greatest perimeter you can make with a rectangle that has an area of 24 square units?

Hint

Hint

What are the possible dimensions of a rectangle that has an area of 24 square units?  How can we determine their perimeter?

Answer

Answer

There are an infinite number of rectangles with an area of 24 square units.  Students may think that a 1 x 24 rectangle has the greatest perimeter, but a .5 x 48 rectangle has an even greater perimeter.  A .25 x 96 rectangle has an even greater perimeter.  So, there is no finite answer.

Source: Robert Kaplinsky

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