Question

exponents, polynomials, and radicals word problem involving the pythagorean theorem in three - dimensions try again... try again (a): your answer is incorrect. 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 = 13 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 = 15.8 in

Explanation:

Step1: Find $a$ using 2 - D Pythagorean theorem

In the base right - triangle with sides 9 in and 12 in, by the Pythagorean theorem $a^{2}=9^{2}+12^{2}$. So, $a^{2}=81 + 144=225$, and $a=\sqrt{225}=15$ in.

Step2: Find $b$ using 3 - D Pythagorean theorem

Now consider the right - triangle with sides $a = 15$ in and 5 in. By the Pythagorean theorem $b^{2}=a^{2}+5^{2}$. Substitute $a = 15$ into the equation: $b^{2}=15^{2}+5^{2}=225 + 25=250$. Then $b=\sqrt{250}\approx15.8$ in.

Answer:

(a) $a = 15$ in
(b) $b\approx15.8$ in