Chapter 12.1, Problem 6WE

To determine

To complete: the table.

Answer to Problem 6WE

$l$	6	50	6	$9$	9	5 $x$
$w$	4	30	3	8	$6$	4 $x$
$h$	2	15	$3$	5	2	3 $x$
$\text{L}\text{.A}\text{.}$	40	$\text{2400}$	$\text{54}$	$\text{170}$	60	$54x^2$
$\text{T}\text{.A}\text{.}$	88	$5400$	$108$	$314$	$168$	$94x^2$
$V$	48	$22500$	54	360	$108$	$60x^3$

Explanation of Solution

Given information:

$l$	6	50	6	?	9	5 $x$
$w$	4	30	3	8	?	4 $x$
$h$	2	15	?	5	2	3 $x$
$\text{L}\text{.A}\text{.}$	?	?	?	?	60	?
$\text{T}\text{.A}\text{.}$	?	?	?	?	?	?
$V$	?	?	54	360	?	?

Calculation: to complete the table,

  $l=5x,w=4x,h=3x$

  $\begin{array}{l}\text{L}\text{.A}\text{.}=ph\\ L.A=\left(5x+4x+5x+4x\right)\text{3}x\text{ [substitute]}\\ L.A=54x^2\text{ [simplify]}\end{array}$

  $\begin{array}{l}V=Bh\\ V=\left(20x^2\right)\left(3x\right)\text{ [substitute]}\\ V=60x^3\text{ [simplify]}\end{array}$

  $\begin{array}{l}\text{T}\text{.A}\text{.=L}\text{.A}+2B\\ \text{T}\text{.A}\text{.}=54x^2+2\left(20x^2\right)\text{ [substitute]}\\ \text{T}\text{.A}\text{.}=94x^2\text{ [simplify]}\end{array}$