Question

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?

Answer 1

We are told that the original square has an area of 81 (cm^2)
`rarr` the original square has dimensions `9` cm `xx 9` cm

If `x` is the amount added/removed from the dimensions, the area of the new rectangle is
`(9-x)(9+x) = 81-x^2`
which, we are told is `9 cm^2` less than the original area of `81 cm^2` (or `72 cm^2`)

So
`81 -x^2 = 72`
`x^2 = 9`
`rarr x=3`