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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#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.