Question

the points j, k, l and m all lie on the same line segment, in that order, such that the ratio of jk : kl : lm is equal to 3 : 1 : 1. if jm = 10, find jl.

Explanation:

Step1: Let the lengths

Let \(JK = 3x\), \(KL=x\), \(LM = x\) (since \(JK:KL:LM = 3:1:1\)).

Step2: Find the value of \(x\)

Since \(JM=JK + KL+LM\), and \(JM = 10\), then \(3x+x + x=10\).
Combining like - terms, we get \(5x=10\).
Dividing both sides by \(5\), \(x=\frac{10}{5}=2\).

Step3: Calculate \(JL\)

Since \(JL=JK + KL\), and \(JK = 3x\), \(KL=x\), then \(JL=3x+x=4x\).
Substitute \(x = 2\) into \(4x\), we get \(JL=4\times2=8\).

Answer:

\(8\)