Use the information and the diagram to answer the question.
Information
A diagram.Short description, A diagram.,Long description,
The diagram shows a triangle, H N M. A line segment, K L, crosses the triangle, and is parallel to base M N. K is on side H M, and L is on side H N. Line segment H K is 3 centimeters, line segment K M is 5 centimeters, and line segment H L is 4 centimeters.
Question
What is the length of segment L N?
Answer options with 4 options
A.
3 and 3-fourths centimeters
C.
6 centimeters
B.
4 centimeters
D.
6 and 2-thirds centimeters
To find the length of segment LN, we can use the fact that line segment KL is parallel to line segment MN. This means that triangles KHL and MNL are similar.
Using the similar triangles, we can set up a proportion to find the length of LN:
LK / MN = LH / NL
Given that LK = 4 centimeters and MN = 5 centimeters, plugging in these values gives us:
4 / 5 = 3 / NL
Now we can solve for NL by cross-multiplying:
4 * NL = 3 * 5
4 * NL = 15
NL = 15 / 4
NL = 3 and 3/4 centimeters
Therefore, the length of segment LN is 3 and 3/4 centimeters.
The correct answer option is A. 3 and 3/4 centimeters.