Final answer:
To find LM, we use the triangle inequality theorem and solve the inequality JL + KL > LM. The answer is 31.
Step-by-step explanation:
To find the value of LM, we need to use the concept of the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we can write the inequality as JL + KL > LM. Substituting the given values, we have 17 + 14 > LM. Solving this inequality, we get LM > 31.
Since we are asked to write the answer as a whole number or decimal rounded to the nearest hundredth, the answer is 31.