Point L is on line segment \overline{KM} KM
. Given LM=3x+3,LM=3x+3, KM=5x+4,KM=5x+4, and KL=5x+1,KL=5x+1, determine the numerical length of \overline{KM}.
KM
.

9514 1404 393

  KM = 4

Step-by-step explanation:

The point of the segment addition postulate is that the combined length of segments laid end-to-end is the sum of their individual lengths.*

  KL +LM = KM

  (5x +1) +(3x +3) = 5x +4

  8x +4 = 5x +4 . . . .simplify

  3x = 0 . . . . . . . . . . subtract 5x+4

  x = 0 . . . . . . . . . . . divide by 3

Then the length of KM is ...

  KM = 5x +4 = 5·0 +4 = 0 +4

  KM = 4

* Sometimes it seems that geometrical theorems simply state the obvious. Some interesting math arises from systems of geometry in which this is not true. We usually don't study those in high school.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.