Answer: To find the value of EF, we can use the fact that the sum of the lengths of two sides of a triangle is always greater than the length of the third side. In this case, we can use the triangle inequality theorem to set up an inequality involving DE, EF, and DF.
Explanation:
According to the triangle inequality theorem, we have:
DE + EF > DF
Substituting the given values, we get:
17 + 9x + 6 > 17x - 9
Next, we simplify and solve for x:
23 + 9x > 17x - 9
9x - 17x > -9 - 23
-8x > -32
x < 4
Now that we have found the value of x, we can substitute it back into the expression for EF to find its value:
EF = 9x + 6
EF = 9(4) + 6
EF = 36 + 6
EF = 42
Therefore, EF is equal to 42.