Question

point k is on line segment $overline{jl}$. given $jl = x + 10$, $kl = 4x$, and $jk = 2x$, determine the numerical length of $overline{kl}$.

Explanation:

Step1: Use segment - addition postulate

Since point K is on line segment $\overline{JL}$, we have $JK + KL=JL$. Substituting the given expressions: $2x + 4x=x + 10$.

Step2: Combine like - terms on the left - hand side

$6x=x + 10$.

Step3: Subtract x from both sides

$6x−x=x + 10−x$, which simplifies to $5x = 10$.

Step4: Solve for x

Dividing both sides by 5, we get $x=\frac{10}{5}=2$.

Step5: Find the length of KL

We know that $KL = 4x$. Substituting $x = 2$ into the expression for KL, we have $KL=4\times2 = 8$.

Answer:

8