Answer:
IK = 13 and x = - 12
Explanation:
Let's write down each segment and if available express it in terms of x which has to be determined in order to find length of segment IK
We have IK = x + 25 (to be determined)
JK = 2x + 30 (1)
KL (unknown)
IL = x + 34 (2)
JL = 15 (3)
The entire segment
IL = IJ + JL
Substituting for JL = 15 we get IL = IJ + 15
But we are given IL = x + 34
IJ + 15 = x + 34
IJ = x + 34 -15 = x + 19 (4)
IK = IJ + JK
Substituting for IJ = x + 19 from equation (4) and JK = 2x + 30 from equation (1) we get IJ + IK = x + 19 + 2x + 30 = 3x + 49
But we are given that IK = x + 25
So
3x + 49 = x + 25
Moving x from the RHS to the LHS and 49 from the LHS to the RHS we get
3x-x = 25 - 49
2x = -24
x = -12
IK = -12 + 25 = 13
We can verify this by finding the lengths of each segment and seeing they are consistent
We have
IJ = x + 19 = -12 + 19 = 7
JK = 2x + 30 = 2(-12) + 30 = -24 + 30 = 6
IL = x + 34 = -12 + 34 = -23
We also have the fact that JK + KL = JL = 15
Substituting for JK we get
6 + KL = 15
KL = 15-6=9
Total segment length = 7+6 + 9 = 22
x + 34 = -12 + 34 = 22
So it is consistent