Calculate the perimeter of a rectangle whose area is 25x² – 35x + 12. 

Given, Area of rectangle = 25x² – 35x + 12

We know the area of a rectangle = length × breadth

So, by factoring 25x² – 35x + 12, the length and breadth can be obtained.

Thus, factoring by using a middle-term split, we get:

= 25x² – 35x + 12 

= 25x² – 15x – 20x + 12

= 5x(5x – 3) – 4(5x – 3)

= (5x – 3)(5x – 4)

So, the length and breadth are (5x – 3) and (5x – 4).

Now, perimeter = 2(length + breadth)

So, 

Perimeter of the rectangle = 2[(5x – 3)+(5x – 4)]

                                               = 2(5x – 3 + 5x – 4) 

                                               = 2(10x – 7) 

                                               = 20x – 14

Thus, the required perimeter = 20x – 14