Answer
$x=4$
Dimensions of the rectangle: $19\,m$ and $11\,m$.
Work Step by Step
$\text{length}\times\text{width}=A$
$\implies (4x+3)(4x-5)=209$
$\implies 16x^{2}-8x-15=209$
$\implies 16x^{2}-8x-224=0$
Identify $a$, $b$, $c$ from the standard form of a quadratic equation:
$a=16, b=-8$ and $c=-224$.
Solve the equation using the Quadratic Formula:
$x=\frac{-b\pm \sqrt {b^{2}-4ac}}{2a}$
$=\frac{-(-8)\pm \sqrt {(-8)^{2}-4(16)(-224)}}{2(16)}$
$\implies x=4$ or $x=-\frac{7}{2}$
Since $\text{length}$ and $\text{width}$ cannot be negative, $x$ should be equal to $4$.
The dimensions of the rectangle are:
$(4x+3)m=[4(4)+3]\,m=19\,m$
$(4x-5)m=[4(4)-5]m=11\,m$
