Question

a gift box has the shape of a right triangular prism. a piece of tape of length ( b ) (in inches) is placed from one corner to the opposite corner, as shown in the figure. (the figure is not drawn to scale.)
(a) find ( a ).
( a = square ) in
(b) use your answer to part (a) to find ( b ), the length of the tape. round your answer to the nearest tenth of an inch.
( b = square ) in

Explanation:

Step1: Calculate $a$ via Pythagoras

$a = \sqrt{9^2 + 12^2}$
$a = \sqrt{81 + 144} = \sqrt{225} = 15$

Step2: Calculate $b$ via Pythagoras

$b = \sqrt{a^2 + 7^2}$
$b = \sqrt{15^2 + 7^2} = \sqrt{225 + 49} = \sqrt{274} \approx 16.6$

Answer:

(a) $a = 15$ in
(b) $b = 16.6$ in