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 Question from nicole, a parent: when given an area, squares are the rectangles with the smallest perimeter write the length and width of the rectangle with the smallest perimeter

Hi Nicole,

This problem is asking you to consider all possible rectangles with the same area. You are not told what the area is so the algebraic technique is to give the area a name, say A, and think of this name (letter) as a number. Each of these rectangles has a certain length and width and we know that the area of a rectangle is the length times the width. Thus if the length is L and the width is W then

L × W = A.

You are also told that among all these rectangles the one with the smallest perimeter is a square. For a square L = W and hence if you can find the length L then you also know the width. For the square

L × W = L × L = L2 = A

The question then come to

If L2 = A what is L?

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.