suppose j is between h and k.use the segment addition postulate to solve for x.then find the length of each segment
hj=5x
jk=7x
kh=96
Hj= 5x-3.
To solve for x using the segment addition postulate, we need to add the lengths of the two smaller segments (hj and jk) to get the length of the larger segment (kh).
Using the segment addition postulate:
kh = hj + jk
Given:
hj = 5x
jk = 7x
kh = 96
Substituting the given values into the equation:
96 = 5x + 7x
Now, we can simplify and solve the equation:
Adding the like terms on the right side:
96 = 12x
Dividing both sides by 12 to isolate x:
x = 96/12
x = 8
Now that we have the value of x, we can substitute it back into the expressions for hj and jk to find their respective lengths:
hj = 5x = 5*8 = 40
jk = 7x = 7*8 = 56
Therefore, the length of segment hj is 40 units and the length of segment jk is 56 units.