Final answer:
To find AD, since DE is the midpoint, AD equals BD which is 4. Then by calculating the full length of AC as AE plus ED, which are both 7, we get AC as 14. AD is then half of AC minus BD, which is 7 - 4 = 3, not matching any of the given options.
Step-by-step explanation:
The question refers to finding the value of AD in a triangle ABC where DE is the midpoint, and we're given BD = 4 and AE = 7.
Since DE is the midpoint of triangle ABC, BD and AD must be equal. Therefore, AD also equals 4. To find the entire length of side AC (which is equal to AE + ED), we know that since DE is the midpoint, ED must also be 7.
As AE = ED and since ED = AD (because DE is the midpoint), we have AE = 7, ED = 7, and AD = 4. Combining ED and AD gives us the entire length of AC, which is AE + ED = 7 + 7 = 14. Thus, AD, which is half of AC, is 14 / 2 = 7, but since we need to subtract BD which is 4, we get AD = 7 - 4 = 3. It seems there might be a misunderstanding or typo because none of the given answer choices match the calculation. Please double-check the question or the provided choices.