Question

In the diagram shown, BD is parallel to AE. What is DE?A. 45 mB. 46.8 mC. 48.6 mD. 50 m

Answer 1

Given that BD is parallel to AE, then triangles CBD and CAE are similar. In consequence, their corresponding sides are in proportion, that is,

`(BC)/(AC)=(DC)/(EC)`

Substituting with data and solving for ED, we get:

`\begin{gathered} (25)/(52+25)=(22.5)/(ED+22.5) \\ (25)/(77)=(22.5)/(ED+22.5) \\ 25\cdot(ED+22.5)=22.5\cdot77 \\ ED+22.5=(1732.5)/(25) \\ ED=69.3-22.5 \\ ED=46.8\text{ m} \end{gathered}`