In the diagram below, start overline, N, O, end overline

Question

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.

Answer 1

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.