Question

c is the midpoint of $overline{bd}$. if $cd = 9x$ and $bd = 10x + 8$, what is $bd?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(C\) is the mid - point of \(\overline{BD}\), then \(BD = 2CD\). Given \(CD = 9x\) and \(BD=10x + 8\), we have the equation \(10x + 8=2\times9x\).

Step2: Solve the equation for \(x\)

\[

$$\begin{align*} 10x + 8&=18x\\ 8&=18x-10x\\ 8&=8x\\ x& = 1 \end{align*}$$

\]

Step3: Find the value of \(BD\)

Substitute \(x = 1\) into the expression for \(BD\). Since \(BD=10x + 8\), then \(BD=10\times1+8=18\).

Answer:

18