SETTING THE SCENE

Recall that we started our story of symmetry with a rectangle of area 36.

Without any further detail, we can say nothing about the width and length \(a\) and \(b\) of that rectangle: maybe it’s a 4-by-9 or a 2-by-18 or a 45-by-0.08 rectangle. We can’t know.

But if we add the word “symmetrical” to our description of the rectangle, then we know something about the values \(a\) and \(b\): they must each be 6.

But there is one other instance where one could say something about the side lengths of a given rectangle.

Suppose I gave you a rectangle and told you it had ZERO AREA.

Then you would say that the picture is wrong and that we should have drawn a “rectangle” with either zero width or zero length. That is, we’d deduce that either \(a=0\) or \(b=0\).

People have observed that this one special case, of having a rectangle of zero area, can be used to solve some certain quadratics—if we are lucky!

This essay shows how.

READ MORE HERE: QUADRATICS PD Essay 3.2

(See too Edfinity.com/XXX for a robust source of curriculum practice problems for you collate, organise, and use.)

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