Question

in the diagram below, cd = 22.5, ce = 28.1, and da = 13.5. find the length of (overline{eb}). round your answer to the nearest tenth if necessary.

Explanation:

Step1: Apply similar - triangle property

Since $\angle CDE=\angle CAB$ and $\angle CED=\angle CBA$ (corresponding angles), $\triangle CDE\sim\triangle CAB$. Then, the ratios of corresponding sides are equal, i.e., $\frac{CD}{CA}=\frac{CE}{CB}$. First, find $CA = CD + DA$.
$CA=22.5 + 13.5=36$

Step2: Set up the proportion

We know that $\frac{CD}{CA}=\frac{CE}{CB}$, substituting the known values: $\frac{22.5}{36}=\frac{28.1}{CB}$. Cross - multiply to get $22.5\times CB=36\times28.1$.
$CB=\frac{36\times28.1}{22.5}$
$CB=\frac{1011.6}{22.5}=44.96$

Step3: Find the length of $EB$

Since $CB = CE+EB$, then $EB=CB - CE$.
$EB = 44.96-28.1 = 16.86\approx16.9$

Answer:

$16.9$