# How can I calculate the length of the longest side of a rectangle and the slope of an imaginary rectangle parallel to the longest side of the first?

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I need a suggestion for this easy but confusing dilemma.

I have a rectangle formed by 4 points (x2,y1) (x1,y2) (x3,y4) (x4,y3). The maximum and minimum are respectively (x4,y4) and (x1,y1).

I need to create a script to obtain the length of the longest side of the rectangle and the slope of an imaginary rectangle parallel to the longest side of the rectangle.

The problem is not so easy taking into account that the rectangle could be in many different positions. I have an idea about the slope, using Pythagoras and the maximum and minimum values, but...the length...I'm stuck on that.

### Accepted Answer

the cyclist
on 17 Oct 2011

I don't understand the part about the slope, but there is an easy way to find the longest side. The distance between each pair of points is

>> dij = sqrt((xi-xj)^2+(yi-yj)^2);

Calculate this for all pairs. You should get three unique length values, corresponding to:

- short side
- long side
- diagonal

The middling value will be the long side of the rectangle.

(You might need to be careful about floating point inexactitudes.)

### More Answers (1)

Image Analyst
on 19 Oct 2011

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