Statement 1: The area of rectangle is x² - 5x + 6 and the longer side of the rectangle is (x - 2).

Statement 2: x² - 5x + 6

= (x - 2) (x - 3)

⇒ for every positive value of x(x > 3), (x - 2) is greater.

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Give, Area of rectangle = x² - 5x + 6

Longer side = (x - 2)

Factorise the area,

⇒ x² - 5x + 6 = 0

⇒ x² - 3x - 2x + 6 = 0

⇒ x(x - 3) - 2(x - 3) = 0

⇒ (x - 2) (x - 3) = 0

So, the given two sides of rectangle are:

(x - 2) (x - 3)

Since x > 3,

∴ (x - 2) > (x - 3)

So, (x - 2) is the longer side.

∴ Both the statements are true.

Hence, option 1 is the correct option.