Answer: JK = 234
Concept:
Here, we need to know the idea of the segment addition postulate.
The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
PART I: Find the value of x
Given information
JL = 8x - 3
LK = 4x + 57
Given expression deducted from the given figure
JL = LK
Substitute values into the expression
8x - 3 = 4x + 57
Add 3 on both sides
8x - 3 + 3 = 4x + 57 + 3
8x = 4x + 60
Subtract 4x on both sides
8x - 4x = 4x + 60 - 4x
4x = 60
Divide 4 on both sides
4x / 4 = 60 / 4
x = 15
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PART II: Find the value of JK
Given information
JL = 8x - 3
LK = 4x + 57
x = 15
Given expression deducted from the segment addition postulate
JK = JL + LK
Substitute values into the expression
JK = 8x - 3 + 4x + 57
JK = 8(15) - 3 + 4(15) + 57
Simplify by multiplication
JK = 120 - 3 + 60 + 57
Simplify by simple operation (addition/subtraction)
JK = 117 + 60 + 57
JK = 177 + 57
Hope this helps!! :)
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