Question

What is the difference in the areas of a square and rectangle if the rectangle has side lengths 2 less and 2 more than

a square? Use algebra or a geometric model to compare the areas and justify your answer.

Answer 1

`A(square) = x*x= x^2`

`A(rectangle) = (a-2) (a+2) = a^2 +2a- 2a-4 = a^2 -4`

`A(rectangle) = A(square) -4`

Explanation:

For this case we assume that the square have sides of length x.

So then the area for this square is given by
`A(square) = x*x= x^2`

We have a rectangle and on this case we have this information :" the rectangle has side lengths 2 less and 2 more than a square"

So then the sides of the rectangle needs to have lengths a-2 and a+2, and if we find the area for the rectangle we got:

`A(rectangle) = (a-2) (a+2) = a^2 +2a- 2a-4 = a^2 -4`

And as we can see th area for the rectangl is 4 units less than the area for the rectangle:

`A(rectangle) = A(square) -4`