Question

How do you use the following formulas for an equation like this?

Answer 1

Let's begin by listing out the information given to us:

|CD| = 9.5, |CE| = 13.75, |AC| = 13.75 + 5.5 = 19.25, |BC| = 9.5 + x

Using Triangle proportionality theorem, we have:

`\begin{gathered} |CE|\colon|EA|=|CD|\colon|DB| \\ 13.75\colon5.5=9.5\colon x\Rightarrow(13.75)/(5.5)=(9.5)/(x) \\ 13.75x=5.5\cdot9.5 \\ (13.75x)/(13.75)=(5.5\cdot9.5)/(13.75)\Rightarrow x=(5.5\cdot9.5)/(13.75) \\ x=3.8 \\ \\ \therefore|BD|=3.8 \end{gathered}`