Question

In triangle ABC, AB=8, BC=10, and AC=12. Let M, N, and K be the midpoints of the sides of triangle ABC. Find the length of each side of MNK.

A) MN=4, NK=5, KM=6
B) MN=5, NK=6, KM=7
C) MN=6, NK=7, KM=8
D) MN=7, NK=8, KM=9

Answer 1

To find the lengths of MN, NK, and KM, we can consider the midpoints as points where the medians of triangle ABC intersect. The length of a median is equal to half the length of the side it is drawn to. Using this information, we can determine that MN = 6, NK = 4, and KM = 5.

Step-by-step explanation:

To find the lengths of MN, NK, and KM, we can consider the midpoints as points where the medians of triangle ABC intersect. Hence, segment MN is the median from vertex A, segment NK is the median from vertex B, and segment KM is the median from vertex C. The length of a median is equal to half the length of the side it is drawn to. Therefore, MN = 1/2 * AC, NK = 1/2 * AB, and KM = 1/2 * BC. Substituting the given side lengths, we get MN = 1/2 * 12 = 6, NK = 1/2 * 8 = 4, and KM = 1/2 * 10 = 5. Hence, the lengths of MN, NK, and KM are 6, 4, and 5 respectively.