Final answer:
To find the smallest whole number value of x for an acute triangle with sides x cm, 2x cm, and 15 cm, we used the Triangle Inequality Theorem. The smallest whole number greater than 5 that satisfies these conditions is 6, which is not listed in the provided options. However, choosing the smallest available option from those provided, the answer is 7.
Step-by-step explanation:
To determine the smallest whole number value of x for which the sides of an acute triangle can be x cm and 2x cm long with the longest side being 15 cm, we can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. In the context of an acute triangle, we also know that all angles are less than 90 degrees, and therefore it is not a right triangle. So, the lengths must satisfy these conditions:
- x + 2x > 15
- x + 15 > 2x
- 2x + 15 > x
The first inequality simplifies to 3x > 15, which implies that x > 5. Since x must be a whole number, the smallest such value that satisfies the inequality is 6, which is not listed in the provided options. However, the question might contain a typo and the original answer options may be incorrect, or the context might have a specific focus on the specific provided answer options. If it's a matter of choosing from the provided options then the smallest one available that is greater than 5 is 7 (option c).