Equable Rectangle

Date: 01/28/2001 at 08:08:07
From: Mark Johnston
Subject: Equable Rectangles

What is the formula for an equable rectangle if I have one side of 
the rectangle? Could you show me how you got your conclusion?

Date: 01/28/2001 at 23:07:46
From: Doctor Peterson
Subject: Re: Equable Rectangles

Hi, Mark.

I take it you want to know the length of one side, x, of a rectangle 
whose other side is a, for which the area is numerically equal to the 
perimeter. 

To find out, just write the formulas for the perimeter and area, set 
them equal, and solve the equation:

    P = 2(a+x)
    A = ax

Solve

    2(a+x) = ax

It's important to realize, as I presume you've been told, that this 
applies only to whatever particular units you have chosen to measure 
in; if you use different units, the same rectangle will no longer be 
"equable" - which is why this is not a real math term, but just an 
idea you're using for this assignment. In fact, ANY rectangle is 
"equable" for some unit.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/