Question

In the following problems, suppose J is between H and K.

• Use Segment Addition Postulate to solve for x.
• Then find the length of each segment.

11. HJ=6x-5
JK=4x-6
KH=129

12. HJ=4x-15
JK=5x-6
KH=15

Please show all work and not just answers.

Answer 1

11. HJ = 79; JK = 50

12. HJ = 1; JK = 14

Explanation:

The segment addition postulate tells you the total length is the sum of the segment lengths.

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11. HJ + JK + HK

(6x -5) +(4x -6) = 129

10x = 140 . . . . add 11

x = 14 . . . . . . . divide by 10

6x -5 = 6(14) -5 = 79 = HJ

4x -6 = 4(14) -6 = 50 = JK

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12. HJ + JK = HK

(4x -15) +(5x -6) = 15

9x = 36 . . . . . add 21

x = 4 . . . . . . . .divide by 9

4(4) -15 = 1 = HJ

5(4) -6 = 14 = JK