Answer
Width: $5$ units
Length: $8$ units
The dimension of the rectangle is $5$ x $8$ units.
Work Step by Step
Let $x = $ the width of the rectangle
$x(x+3) = 40$
$x^{2} + 3x = 40$
$x^{2} + 3x - 40 = 0$
Find two numbers that can be multiplied together to get $-40$ and can be added together to get $3$.
$= -5$ and $8$
$x^{2} - 5x + 8x - 40 = 0$
$x(x - 5) + 8(x-5) = 0$
$(x+8)(x-5) = 0$
$x = -8, 5$
Given that $x \ne -8$, then $x = 5$ units.
Width: $5$ units
Length: $x + 3$
$= 5 + 3$
$= 8$ units