Answer: 27
Explanation:
To find the value of MN, you can use the information given in the problem.
You have:
1. LM = 13
2. MN = x + 15
3. LN = 3x + 4
The sum of the lengths of two sides of a triangle must be greater than the length of the third side. In this case, LM + MN > LN.
So, we can write the inequality:
13 + (x + 15) > (3x + 4)
Now, let's solve for x:
13 + x + 15 > 3x + 4
Combine like terms:
x + 28 > 3x + 4
Subtract x from both sides:
28 > 2x + 4
Subtract 4 from both sides:
24 > 2x
Now, divide by 2:
12 > x
So, x is less than 12.
Now, you can find MN by substituting this value back into the expression for MN:
MN = x + 15
MN = 12 + 15
MN = 27
Therefore, MN is equal to 27.