Question

1. the length of $overline{ac}$ is equal to $5x + 8$. given the diagram below, determine its actual length.

a $x + 3$ d $2x + 9$ c

Explanation:

Step1: Set up equation

Since $AC = AD + DC$, we have $5x + 8=(x + 3)+(2x+9)$.

Step2: Simplify right - hand side

Combine like terms: $(x + 3)+(2x+9)=x+2x + 3+9=3x + 12$. So the equation becomes $5x + 8=3x+12$.

Step3: Solve for x

Subtract $3x$ from both sides: $5x-3x + 8=3x-3x+12$, which simplifies to $2x+8 = 12$. Then subtract 8 from both sides: $2x+8 - 8=12 - 8$, getting $2x=4$. Divide both sides by 2: $x = 2$.

Step4: Find length of AC

Substitute $x = 2$ into the expression for $AC$: $AC=5x + 8=5\times2+8=10 + 8=18$.

Answer:

18