Final Answer:
The midsegment DE is parallel to AC and half its length, making AC equal to 2 times DE. Given that DE is 5, AC is calculated as 2 * 5, resulting in AC = 10. The value of AC is 10.
Step-by-step explanation:
D and E being midpoints of sides AB and BC, respectively, means DE is a midsegment of triangle ABC. In a triangle, a midsegment is parallel to the third side and half its length. Therefore, DE being 5 implies BC is twice that, making BC equal to 10.
As DE connects the midpoints, it's also parallel to AC. Now, AC is the sum of BC and AB. Since BC is 10, and DE is parallel to AC, the other half of AC is AB. Therefore, AB is also 10. Adding BC and AB, we get AC as 20. However, since DE is only 5, it means BC and AB are each 5, leaving AC as the sum of BC and AB, which is 10.
Now, since DE is parallel to AC and is a midsegment, it divides AC into two equal parts. This means that the other half of AC is represented by the length of AB. So, AB is also 5. The total length of AC is the sum of BC and AB. Substituting the values we have, AC = BC + AB, and AC = 10 + 5, resulting in AC = 15.
However, there seems to be a contradiction as DE is stated to be 5. Re-evaluating, it becomes clear that DE is parallel to AC and represents only half of AC. Therefore, AC is twice DE, making AC equal to 10. Hence, the final value of AC is 10.
Therefore, the correct answer is The value of AC is 10.