Equable shapes

[Alistair S Ross]

My daughters math's homework was on equable shapes. The example given at
school was a square with 4cm sides so the perimeter is 16cm and the area
is 16 sq cm. This was the only equable shape that I could find, which is
probably why it was given as an example. What are the ways/tricks of
finding equable shapes other than doing it "long hand".

Cheers....ttfn....Alistair
--
: Alistair S Ross
: Room W7b, Instrument Shop, C.U.E.D.
: phone - UK(01223)332853
: email - a...@eng.cam.ac.uk

[Biff Vernon]

In an equable shape area, a = perimeter, p
so a=p
For rectangles area =length, l times breadth, b
so a=lb
and perimeter = twice length plus breadth
so p = 2(l+b)
so for equable rectangles lb = 2(l+b)
enter this equation into a graphic calculator with an equation colving
capabilities and all the answers will be produced.
Failing this set up a spreadsheet
Column 1 for length
column 2 for breadth
column 3 for area: =A1*B1
column 4 for perimeter: =2*(A1+B1)
column 5 difference of cols. 3 & 4: =C1-D1
Col 5 checks to see if area and perimeter are equall and returns 0 if they
are.
Now choose a length and then, by trial and improvement, find a breadth. You
can tell if your improvements are going in the right direction by lookin at
col 5 to see if you are approaching 0 from negative or positive side. A bit
of Fill Down on the spreadsheet enables the search to proceed very quickly.
Try plotting a graph of ALL the equable rectangles with length against
breadth.
Then try other shapes. For triangles change the perimeter formula to a+b+c
and area to .....oh dear...what's an easy formula for the area of any
triangle?

Alistair S Ross <a...@eng.cam.ac.uk> wrote in article
<345765FB...@eng.cam.ac.uk>...