Explanation:
Based on the information given in the diagram, we know that AABD and ACAD are similar triangles, which means their corresponding sides are proportional.
Let's denote the length of AD as x. According to the similarity of the triangles, we can set up the following proportion:
AB/AC = AD/AD
Since AD is common to both triangles and has a length of x, the proportion simplifies to:
AB/AC = 1
We are given that AB = 12, so we can substitute that value into the proportion:
12/AC = 1
To solve for AC, we can cross-multiply:
12 = AC
Therefore, the value of x in the figure is 12.