Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19.6

Question

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Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19.6

meters. The lengths of J N and N L are 7.4 meters. The lengths of K M and M L are 10.7 meters.
What is the distance between points M and N?

meters

Mathematics

1 answer:

Kruka [31] · Answer 1 · 2023-07-11T13:37:55+03:00

The distance between points M and N according to the task content is; 9.8 meters.

<h3>What is the distance between points M and N?</h3>

From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints KL and JL respectively.

Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;

NM/19.6 = 7.4/(2×7.4)

NM = 19.6/2 = 9.8 meters.

This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.