Final answer:
Using the Pythagorean theorem to solve the right triangle problem, Zack will need 15 meters of garland to cover the length of the ballroom ceiling, which is confirmed to be option (c).
Step-by-step explanation:
Zack is facing a classic right triangle problem in decorating the ballroom ceiling. To find the length, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²). Given that the width of the ceiling is 8 meters (a) and the diagonal is 17 meters (c), we can find the length of the ceiling (b) by rearranging the formula to b² = c² - a² and then taking the square root of both sides.
Thus, the calculation will be as follows:
- b² = 17² - 8²
- b² = 289 - 64
- b² = 225
- b = √225
- b = 15 meters
Therefore, Zack will need 15 meters of garland for the length of the ceiling, which corresponds to option (c).