Chapter 12.2, Problem 4WE

To determine

To complete: the table.

Answer to Problem 4WE

Height, $h$	4	12	24	$3\sqrt{7}$	?	6
Slant height, $l$	5	13	$25$	12	5	?
Base edge	$\text{6}$	$10$	14	$18$	8	?
Lateral edge	$\sqrt{34}$	$\sqrt{194}$	$\sqrt{674}$	15	?	10

Explanation of Solution

Given information:

Height, $h$	4	12	24	?	?	6
Slant height, $l$	5	13	?	12	5	?
Base edge,	?	?	14	?	8	?
Lateral edge	?	?	?	15	?	10

Calculation: to complete the table,

  $l=12,\text{lateral edge}=15$

  $\begin{array}{l}\text{lateral edge}=\sqrt{{\left(l\right)}^2+{\left(\frac{\text{base edge}}{2}\right)}^2}\\ \text{15}=\sqrt{{\left(12\right)}^2+{\left(\frac{\text{base edge}}{2}\right)}^2}\text{ [substitute]}\\ \text{225}=144+{\left(\frac{\text{base edge}}{2}\right)}^2\text{ [square]}\\ {\left(\frac{\text{base edge}}{2}\right)}^2=81\text{ [subtract]}\\ \frac{\text{base edge}}{2}=9\text{ [sqaure root]}\\ \text{base edge}=18\text{ [multiply]}\end{array}$

  $\begin{array}{l}\text{Base edge}=2\sqrt{{\left(l\right)}^2-{\left(h\right)}^2}\\ \text{18}=2\sqrt{{\left(12\right)}^2-{\left(h\right)}^2}\text{ [substitute]}\\ 9=\sqrt{144-h^2}\text{ [square and divide]}\\ 144-h^2=81\text{ [square]}\\ h=3\sqrt{7}\text{ [simplify]}\end{array}$