a gift box has the shape of a right triangular prism. a piece of tape of length (b) (in inches) is placed…
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
Answer
Explanation:
Step1: Find the length of the base - diagonal (a)
In the base right - triangle with sides 9 in and 12 in, use the Pythagorean theorem (c=\sqrt{a^{2}+b^{2}}). Here, (a = 9) and (b = 12), so (a=\sqrt{9^{2}+12^{2}}). [a=\sqrt{81 + 144}=\sqrt{225}=15]
Step2: Find the length of the tape (b)
Now consider a right - triangle with sides 5 in and the base - diagonal (a = 15) in. Again, use the Pythagorean theorem (b=\sqrt{5^{2}+a^{2}}). Substitute (a = 15) into the formula: (b=\sqrt{5^{2}+15^{2}}=\sqrt{25 + 225}=\sqrt{250}\approx15.8)
Answer:
(a) (a = 15) (b) (b\approx15.8)