Final answer:
The length of segment DF in triangle DEF is 9√7.
Step-by-step explanation:
The length of segment DF in triangle DEF can be found using the Pythagorean theorem. Based on the information given in the question, we can assume that segment DE and segment EF are the other two sides of the triangle. To find the length of segment DF, we use the formula: DF^2 = DE^2 + EF^2.
Let's assume that DE is 18, and EF is 9√3. Plugging the values into the formula, we have: DF^2 = 18^2 + (9√3)^2.
Calculating the square of the values, DF^2 = 324 + 243 = 567. Taking the square root of both sides, DF = √567 = 3√63 = 3√(9 x 7) = 3 x 3√7 = 9√7.
Therefore, the length of segment DF is 9√7.