Final answer:
Without the orientation of the triangle in the question, it is not possible to definitively determine whether PQ represents the side with a length of 8 cm or 15 cm. However, option c (17 cm) is incorrect as it represents the hypotenuse, and option d (23 cm) is unrelated to the given side lengths.
Step-by-step explanation:
To find the value of PQ, which is a side of a right triangle, we can use the Pythagorean theorem. The theorem 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 (a and b). This relationship is represented by the equation a² + b² = c².
Given that a = 15 cm, b = 8 cm, and c = 17 cm, we can check if the given sides satisfy the Pythagorean theorem. Calculating the square of the lengths of sides a and b gives us:
- a² = 15² = 225
- b² = 8² = 64
- a² + b² = 225 + 64 = 289
The square of the hypotenuse (c²) should also be 289, since c = 17 cm and 17² = 289. Therefore, the values of a, b, and c satisfy the Pythagorean theorem, and the sides are correctly identified where c is the hypotenuse.
So, the value of PQ, could either be side a or b depending upon the triangle orientation, but since PQ cannot be the hypotenuse, PQ cannot be 17 cm. It must be 8 cm or 15 cm, and without further context on which side PQ refers to within the triangle, we cannot definitively select between options a and b. However, the options provided do not consider the ambiguity, suggesting the question may have a typographical error or a missing diagram. Option c (17 cm) represents the hypotenuse, which PQ is not, and option d (23 cm) is not relevant to the given side lengths.