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### Rectangles: Area and Perimeter the Same

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Date: 4/15/96 at 22:20:22
From: Anonymous
Subject: Problem solving

There are two different rectangles whose sides are integers and
whose area and perimeter are the same.  Find the dimensions.
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Date: 4/16/96 at 10:17:11
From: Doctor Sebastien
Subject: Re: Problem solving

Let x and y be the sides of the rectangle.

The area is xy and the perimeter is 2(x+y)
xy = 2x + 2y
xy - 2x - 2y = 0
x(y-2) = 2y
x = 2y/(y-2)

Now find values of x and y such that x>0, y>0 and x and y are
integers.

When y = 3, x = 6.
When y = 4, x = 4

-Doctor Sebastien,  The Math Forum

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Associated Topics:
Middle School Algebra
Middle School Geometry
Middle School Triangles and Other Polygons

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