point k is on line segment $overline{jl}$. given $jl = x + 10$, $kl = 4x$, and $jk = 2x$, determine the…
point k is on line segment $overline{jl}$. given $jl = x + 10$, $kl = 4x$, and $jk = 2x$, determine the numerical length of $overline{kl}$.
Answer
Explanation:
Step1: Use segment - addition postulate
Since point K is on line segment $\overline{JL}$, we know that $JK + KL=JL$. Substitute 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
Divide both sides by 5: $x=\frac{10}{5}=2$.
Step5: Find the length of $\overline{KL}$
We know that $KL = 4x$. Substitute $x = 2$ into the expression for $KL$. So $KL=4\times2 = 8$.
Answer:
8