# The area of a rectangle is expressed by the polynomial A(x) = 6x^2+17x+12. What is the perimeter of this rectangle?

Jun 6, 2018

$P \left(x\right) = 10 x + 14$

#### Explanation:

The area of a rectangle is found from $A = l \times b$

We therefore need to find the factors of the polynomial.

$A \left(x\right) = 6 {x}^{2} + 17 x + 12$

$A \left(x\right) = \left(3 x + 4\right) \left(2 x + 3\right)$

We cannot get numerical values for the length and breadth, but we have found them in terms of $x$.

$l = \left(3 x + 4\right) \mathmr{and} b = \left(2 x + 3\right)$

$P = 2 l + 2 b$

$P \left(x\right) = 2 \left(3 x + 4\right) + 2 \left(2 x + 3\right)$

$P \left(x\right) = 6 x + 8 + 4 x + 6$

$P \left(x\right) = 10 x + 14$