Question

1. points j, k, and l are on a line segment. k is between j and l. if jk = 4x and kl = x + 12, and jl = 27, what is the length of kl?

a) 3
b) 12
c) 15
d) 27
○ a) 3
○ b) 12
○ c) 15
○ d) 27

Explanation:

Step1: Use segment - addition postulate

Since $K$ is between $J$ and $L$, we have $JK + KL=JL$. Substitute the given expressions: $4x+(x + 12)=27$.

Step2: Simplify the left - hand side

Combine like terms: $4x+x+12 = 5x+12$. So, $5x+12 = 27$.

Step3: Solve for $x$

Subtract 12 from both sides: $5x=27 - 12$, which gives $5x=15$. Then divide both sides by 5: $x=\frac{15}{5}=3$.

Step4: Find the length of $KL$

Substitute $x = 3$ into the expression for $KL$. Since $KL=x + 12$, then $KL=3+12=15$.

Answer:

C. 15