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I'mIf a room is 8x8 meter the perimeter will be 32m, and 64m2. If add 2m on two sides and subtract 2m on two sides the room will be 10x6m. The perimeter, and footprint, will be the same for both rooms but the square meters will be different, can someone please explain this? I must be missing some fundamental logic here...

Kjetil
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Perimeter is the length of the boudary of a region, but, area covers the whole region. Your figure makes a square and a rectangle, both of which will give different area. It's just a co-incidence that you get the same perimeter. Figures will clear your doubts.

Utkarsh
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  • This is applicable inn all situations, if you add X meters on two sides and subtract the same X on two sides the perimeter will stay the same. But the square meter will never be the same. Can you show me the math? – Kjetil Jun 03 '16 at 14:45
  • @Kjetil $x^2\ne(x+2)(x-2)=x^2-4$. – almagest Jun 03 '16 at 14:47
  • I'm sorry, I will need some figures to understand this -_- – Kjetil Jun 03 '16 at 14:51
  • Let us suppose a square of side xx. If we add a metres to two sides and remove a metres from any two sides (remember a<x), it becomes a rectangle of (x+a)(x-a). You must be knowing that adding a certain number to a set values and removing the same number from same number of values will not effect their sum. So, perimeter remains unaffected which is the sum of length of sides. But, area becomes (x+a)(x-a) which is not equal to x*x – Utkarsh Jun 03 '16 at 16:44