# If the same amount is added to one dimensions and removed from the other, the resulting rectangle has an area of 9 square centimeters less than the area of the square which is 81, how much is added and subtracted?

Mar 27, 2015

We are told that the original square has an area of 81 (cm^2)
$\rightarrow$ the original square has dimensions $9$ cm $\times 9$ cm

If $x$ is the amount added/removed from the dimensions, the area of the new rectangle is
$\left(9 - x\right) \left(9 + x\right) = 81 - {x}^{2}$
which, we are told is $9 c {m}^{2}$ less than the original area of $81 c {m}^{2}$ (or $72 c {m}^{2}$)

So
$81 - {x}^{2} = 72$
${x}^{2} = 9$
$\rightarrow x = 3$