To find AD in triangle ABC, we can use the ratio of the lengths of corresponding sides and the fact that the heights are proportional. By setting up and solving two equations, we can find the value of AD.
In triangle ABC, we have AU = 16, BU = 12, and CF = 18. To find AD, we can use the property of triangles that the ratio of the lengths of corresponding sides is equal to the ratio of their corresponding heights. In this case, we can use the ratios AU/BU = AD/BD and CF/BU = AD/CD.
Substituting the given values, we get: 16/12 = AD/BD and 18/12 = AD/CD.
Simplifying these ratios, we have 4/3 = AD/BD and 3/2 = AD/CD
Since BD and CD add up to AD, we can write the equation: AD = BD + CD.
Substituting the values, we get: AD = (4/3)BD + (3/2)CD.