Question

what is the length of $overline{bd}$ if $cb = 7x + 12$, $bd = 6x + 14$, and $cd = 65?
c b d
(not drawn to scale)
a 7
b 3
c 32
d 33

Explanation:

Step1: Use segment - addition postulate

Since $CD = CB+BD$, we substitute the given expressions: $65=(7x + 12)+(6x + 14)$.

Step2: Combine like - terms

$65 = 7x+6x+12 + 14$, so $65=13x + 26$.

Step3: Solve for x

Subtract 26 from both sides: $65−26=13x$, which gives $39 = 13x$. Then divide both sides by 13: $x=\frac{39}{13}=3$.

Step4: Find the length of BD

Substitute $x = 3$ into the expression for $BD$. $BD=6x + 14$, so $BD=6\times3+14=18 + 14=32$.

Answer:

C. 32