Question

1. (image of a rectangular prism with length 12, width 9, height 8, and a diagonal labeled x)

Explanation:

Step1: Find base diagonal first

Let base diagonal be $d$. Use Pythagoras:
$d = \sqrt{12^2 + 9^2}$
$d = \sqrt{144 + 81} = \sqrt{225} = 15$

Step2: Find space diagonal $x$

Use Pythagoras with height 8:
$x = \sqrt{d^2 + 8^2}$
$x = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289}$

Answer:

17