Question

l is the midpoint of $overline{km}$. if $kl = x + 10$ and $km = 4x + 4$, what is $kl$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since $L$ is the mid - point of $\overline{KM}$, we know that $KL=\frac{1}{2}KM$. So, $2KL = KM$. Substituting the given expressions, we get $2(x + 10)=4x+4$.

Step2: Expand the left - hand side

Using the distributive property $a(b + c)=ab+ac$, we have $2x+20 = 4x + 4$.

Step3: Isolate the variable terms

Subtract $2x$ from both sides: $2x+20-2x=4x + 4-2x$. This simplifies to $20 = 2x+4$.

Step4: Isolate the constant terms

Subtract 4 from both sides: $20 - 4=2x+4 - 4$. So, $16 = 2x$.

Step5: Solve for $x$

Divide both sides by 2: $\frac{16}{2}=\frac{2x}{2}$. Thus, $x = 8$.

Step6: Find the value of $KL$

Substitute $x = 8$ into the expression for $KL$. Since $KL=x + 10$, then $KL=8 + 10=18$.

Answer:

18