In the diagram below, start overline, N, O, end overline
NO
is parallel to start overline, K, L, end overline
KL
. If L, O, equals, 4LO=4, N, O, equals, 3NO=3, and K, L, equals, 6KL=6, find the length of start overline, M, O, end overline
MO
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Since NO is parallel to KL, we can use the concept of similar triangles.
From the given information, we know that 4LO = 4NO = 3NO. This implies that 4LO = 4NO = 3NO = 4x, where x is the length of NO.
Similarly, we have KL = 6KL = 6NO = 6x.
We can set up the proportion:
LO/MO = KL/NO
4x/MO = 6x/x
4x/MO = 6
MO = (4x)/6
MO = (2x)/3
Since NO = x, we can substitute back into the equation:
MO = (2x)/3 = (2NO)/3
Therefore, the length of MO is (2NO)/3 or (2x)/3.