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

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20x - 11

20x - 19

22x - 13

20x - 14

answer is B.

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Detailed Solution

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

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