Answer:
FD = 3.16
Explanation:
To determine the length of FD, we can use the property of similar triangles that corresponding sides are in proportion to each other. That is,
AB/DE = BC/EF = CA/FD
We are given the lengths of AB, CA, and BC in triangle ABC, and we know that triangle ABC is similar to triangle DEF. We can use the first two sides to find the third side of triangle DEF as follows:
AB/DE = 11/DE = 7.9/EF
=> EF = (DE * 7.9) / 11
Next, we can use the third proportionality to find FD:
CA/FD = 7.6/FD = 11/EF
=> FD = (11 * 7.6) / EF
=> FD = (11 * 7.6) / ((DE * 7.9) / 11)
=> FD = (11^2 * 7.6) / (DE * 7.9)
Now, we just need to substitute the given values and solve for FD:
FD = (11^2 * 7.6) / (4.4 * 7.9)
FD = 3.16
Therefore, the length of FD is 3.16.