A rectangular piece of paper would lose 999cm2999cm2 of area if a 3cm3cm wide border was trimmed from all four sides.If instead the trimmed border was 2cm2cm wide, what area, in square centimetres, would be lost?

The problem states that a rectangular piece of paper would lose 999 cm^2 of area if a 3 cm wide border was trimmed from all four sides. This means that the length and width of the paper are each reduced by 6 cm (3 cm from each side).

Let's denote the original length of the paper as L and the original width as W. After trimming, the length becomes (L-6) and the width becomes (W-6). The area of the trimmed rectangle is therefore (L-6)*(W-6).

According to the problem, the area of the original rectangle minus the area of the trimmed rectangle equals 999 cm^2. This can be written as:

LW - (L-6)(W-6) = 999

Expanding the right side of the equation gives:

LW - (LW - 6L - 6W + 36) = 999

Simplifying gives:

6L + 6W - 36 = 999

Dividing through by 6 gives:

L + W - 6 = 166.5

So, the sum of the original length and width of the paper is 166.5 cm.

Now, if instead the trimmed border was 2 cm wide, the length and width of the paper would each be reduced by 4 cm (2 cm from each side). The area of this new trimmed rectangle is (L-4)*(W-4).

The area lost due to this new trimming is therefore:

LW - (L-4)(W-4)

Expanding the right side of the equation gives:

LW - (LW - 4L - 4W + 16)

Simplifying gives:

4L + 4W - 16

Substituting L + W = 166.5 into this equation gives:

4*166.5 - 16 = 650 cm^2

So, if the trimmed border was 2 cm wide, 650 cm^2 of area would be lost.