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

Given,

Area of rectangle = $25{\mathrm{x}}^2-35\mathrm{x}+12,$

We know, the area of a rectangle = length × breadth

So, by factoring $25{\mathrm{x}}^2-35\mathrm{x}+12,$ the length and breadth can be obtained.

$25{\mathrm{x}}^2-35\mathrm{x}+12= 25{\mathrm{x}}^2-15\mathrm{x}-20\mathrm{x}+12$

$\Rightarrow 25{\mathrm{x}}^2-35\mathrm{x}+12=5\mathrm{x}(5\mathrm{x}-3)-4(5\mathrm{x}-3)$

$\Rightarrow 25{\mathrm{x}}^2-35\mathrm{x}+12=(5\mathrm{x}-3)(5\mathrm{x}-4)$

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

Now, perimeter = 2(length + breadth)

$\mathrm{Perimeter} \mathrm{of} \mathrm{the} \mathrm{rectangle} = 2\left[\right(5\mathrm{x}-3)+(5\mathrm{x}-4\left)\right]$

$= 2(5\mathrm{x}-3+5\mathrm{x}-4)=2(10\mathrm{x}-7)=20\mathrm{x}-14$

So, the perimeter = 20x – 14