Question

1. if (ab = 2x - 2) and (bc=x + 5), and (ac = 36), find (overline{ab}) and (overline{bc}).

Explanation:

Step1: Use segment - addition postulate

Since $AC=AB + BC$, we substitute the given expressions: $(2x - 2)+(x + 5)=36$.

Step2: Combine like - terms

$2x-2+x + 5=36$ simplifies to $3x+3 = 36$.

Step3: Isolate the variable term

Subtract 3 from both sides: $3x+3-3=36 - 3$, so $3x=33$.

Step4: Solve for x

Divide both sides by 3: $\frac{3x}{3}=\frac{33}{3}$, then $x = 11$.

Step5: Find the length of $\overline{AB}$

Substitute $x = 11$ into the expression for $AB$: $AB=2x-2=2\times11-2=22 - 2=20$.

Step6: Find the length of $\overline{BC}$

Substitute $x = 11$ into the expression for $BC$: $BC=x + 5=11+5=16$.

Answer:

$\overline{AB}=20$, $\overline{BC}=16$