Chapter 12.2, Problem 3WE

To determine

To complete: the table.

Answer to Problem 3WE

Height, $h$	4	12	24	?	?	6
Slant height, $l$	5	13	$25$	12	5	?
Base edge	$\text{6}$	$10$	14	?	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,

  $h=24,\text{base edge}=14$

  $\begin{array}{l}\text{Base edge}=2\sqrt{{\left(l\right)}^2-{\left(h\right)}^2}\\ \text{14}=2\sqrt{{\left(l\right)}^2-{\left(24\right)}^2}\text{ [substitute]}\\ \text{7}=\sqrt{l^2-576}\text{ [square and divide]}\\ l^2-576=49\text{ [square]}\\ l=25\text{ [simplify]}\end{array}$

  $\begin{array}{l}\text{lateral edge}=\sqrt{{\left(l\right)}^2+{\left(\frac{\text{base edge}}{2}\right)}^2}\\ \text{lateral edge}=\sqrt{{\left(25\right)}^2+{\left(7\right)}^2}\text{ [substitute]}\\ \text{lateral edge}=\sqrt{674}\text{ [simplify]}\end{array}$