CUANTO ES x + y = 3
2x + y = 0

 x + y = 3
 2x + y = 0​

The length of each side of the square = (3x - 2) units

The dimensions of the rectangle = (5x + 4y) units & (5x - 4y) units

Step-by-step explanation:

Part A

Given:

Area of square = (9x^2 - 12x + 4) sq. units

To find:

The length of each side of the square = ?

Solution:

9x^2 - 12x + 4 = 0

(3x)^2 - 2(3x)(2) + (2)^2 = 0

(3x - 2)^2 = 0   {Applying a^2 - 2ab + b^2 = (a - b)^2}

3x - 2 = 0        3x - 2 = 0

Therefore,

The length of each side of the square = (3x - 2) units

Part B

Given:

Area of rectangle = (25x^2 - 16y^2) sq. units

To find:

The dimensions of the rectangle = ?

Solution:

25x^2 - 16y^2 = 0

(5x)^2 - (4y)^2 = 0

(5x + 4y)(5x - 4y) = 0  {Applying a^2 - b^2 = (a + b)(a - b)}

Therefore,

The dimensions of the rectangle = (5x + 4y) units & (5x - 4y) units