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: Find $a$ using Pythagorean theorem

In the right - angled triangle on the base with sides 5 in and 12 in, by the Pythagorean theorem $a^{2}=5^{2}+12^{2}$.
$a^{2}=25 + 144=169$.
Taking the square root of both sides, $a=\sqrt{169}=13$ in.

Step2: Find $b$ using Pythagorean theorem

Now consider the right - angled triangle with sides $a = 13$ in and 8 in. By the Pythagorean theorem $b^{2}=a^{2}+8^{2}$.
Since $a = 13$, then $b^{2}=13^{2}+8^{2}=169+64 = 233$.
Taking the square root of both sides, $b=\sqrt{233}\approx15.3$ in.

Answer:

(a) $a = 13$ in
(b) $b\approx15.3$ in