Difference of squares: Worded problems

The length of the side of a square is X cm

(x>3)

Extend one side by 3 cm and shorten an adjacent side by 3 cm to obtain a rectangle.

Express the area of the rectangle using x.

$x^2-9\left(\operatorname{cm}²\right)$

The length of the side of the square $x+1$ cm

(x>3)

We extend one side by 1 cm and shorten an adjacent side by 1 cm, and we obtain a rectangle.

What is the area of the rectangle?

$x^2+2x$

The length of the square is equal to $x$ cm

(x>1) We extend one side by 3 cm and shorten an adjacent side by 1 cm and we obtain a rectangle,

What is the length of the side of the given square if it is known that the two areas are equal?

$x=\frac{3}{2}cm$

The side length of a square is X cm

(x>3)

We extend one side by 3 cm and shorten an adjacent side by 3 cm, and we get a rectangle.

Which shape has a larger area?

The square