a gift box has the shape of a right triangular prism. a piece of tape of length b (in inches) is placed from…
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 = 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 = in
Answer
Explanation:
Step1: Find $a$ using Pythagorean theorem
In the right - triangle on the base with sides 5 in and 12 in, by the Pythagorean theorem $a^{2}=5^{2}+12^{2}$. $a^{2}=25 + 144=169$. So, $a=\sqrt{169}=13$ in.
Step2: Find $b$ using Pythagorean theorem
Now, consider the right - triangle with sides $a = 13$ in and 13 in to find $b$. By the Pythagorean theorem $b^{2}=a^{2}+13^{2}$. Since $a = 13$, then $b^{2}=13^{2}+13^{2}=169+169 = 338$. $b=\sqrt{338}\approx18.4$ in.
Answer:
a = 13 in b = 18.4 in