Question

if (bc = 5x), (cd=8x - 2), and (bd = 12x + 9), what is (bd)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $BD=BC + CD$, we have the equation $12x + 9=5x+(8x - 2)$.

Step2: Simplify the right - hand side of the equation

$5x+(8x - 2)=5x + 8x-2=13x - 2$. So the equation becomes $12x + 9=13x - 2$.

Step3: Solve for x

Subtract $12x$ from both sides: $12x+9-12x=13x - 2-12x$, which gives $9=x - 2$. Then add 2 to both sides: $9 + 2=x-2 + 2$, so $x = 11$.

Step4: Find the length of BD

Substitute $x = 11$ into the expression for $BD$. Since $BD=12x + 9$, then $BD=12\times11+9$.
$BD=132 + 9=141$.

Answer:

$141$