Chapter 8.5, Problem 63PFA

To determine

To find how tall Ashely’s box can be, where surface area is 214, length is 7 and width is 6 in the formula $S=2w\left(l+h\right)+2lh$ .

Answer to Problem 63PFA

  $h=5$

Explanation of Solution

Given information:

  $\begin{array}{l}S=2w\left(l+h\right)+2lh\\ S=214\\ l=7\\ w=6\end{array}$

Calculation:

In order to find how tall Ashley’s box, that is the height of the box, first substitute the values of width, length and surface area in the formula of surface area, that is $S=2w\left(l+h\right)+2lh$ and then the equation is:

  $\begin{array}{l}S=2w\left(l+h\right)+2lh\\ 214=2\left(6\right)\left(7+h\right)+2\left(7\right)h\\ 214=12\left(7+h\right)+14h\\ 214=84+12h+14h\\ 214=84+26h\end{array}$

Now to find the value of h from the equation, first subtract 84 from both sides and then divide both sides by 26 to simplify further as shown below:

  $\begin{array}{l}214=84+26h\\ 214-84=84-84+26h\\ 130=26h\\ \frac{130}{26}=\frac{26h}{26}\\ 5=h\\ h=5\end{array}$

So, the box can be 5 inches tall.