Question

MN and KL are parallel. If JM=9, MK=45, and LN=40, what is NJ?

Answer 1

The length of segment of NJ in the similar triangles is determined as 8. (Option B).

How to calculate length of NJ?

The length of segment of NJ is calculated by applying similar triangle principle as follows;

JM / MK = NJ / LN

The given parameters include;

• length of segment JM = 9
• length of segment MK = 45
• length of segment LN = 40

The value of segment of NJ is calculated by substituting the value of each of the given line segments as follows;

9 / 45 = NJ / 40

NJ = 40 x (9 /45)

NJ = 8

Thus, we can conclude that the length of segment of NJ is determined as 8.

Answer 2

Answer: NJ = 8

Explanation:

Given: In triangle JKL , MN is a line segment parallel to KL intersects the other sides into two distinct points at M and N.

The basic proportionality theorem says that a line is parallel to a side of a triangle which intersects the other sides into two different points then the line divides those sides in proportion.

So by basic proportionality theorem we have :-

`(JM)/(MK)=(NJ)/(LN)\\\\\Rightarrow(9)/(45)=(NJ)/(40)\\\\\Rightarrow NJ=(40)/(5)\\\\\Rightarrow NJ=8`