Answer
The solution is $l=21.6, w=7.2, \text{ and } h=14.4$ or $(21.6, 7.2, 14.4)$.
Work Step by Step
Label the original equations:
1. $2l + 2w + h = 72$
2. $l = 3w$
3. $h = 2w$
Substitute the expressions for $l$ and $h$ given by equations $2$ and $3$, respectively, into equation $1$:
$2(3w) + 2w + (2w) = 72$
$6w + 2w + 2w = 72$
$10w = 72$
Divide both sides of the equation by $10$:
$w = 7.2$
Substitute this value for $w$ into equation $2$ to find $l$:
$l = 3(7.2)$
$l = 21.6$
Substitute the value for $w$ into equation $3$ to find $h$:
$h = 2(7.2)$
$h = 14.4$
The solution is $(21.6, 7.2, 14.4)$.
