#### Answer

The height of the rocket motor is 13 meters.
The diameter of the rocket motor is 1 meter.

#### Work Step by Step

Let $h$ be the height of the rocket motor.
Let $d$ be the diameter of the rocket motor.
$h=8+5d$
$h+d=14$
$8+5d+d=14$
$8+6d=14$
$6d=6$
$d=1$
$h=8+5d$
$h=8+5(1)$
$h=13$