Refer to the image in the link, in which angles $ABE$ and $CDE$ are equal in size, and various segments have been marked with their lengths. Find $x$.
I thought that $\bigtriangleup CDE$ is similar to $\bigtriangleup CAB$, therefore, I made the following proportions $\frac{CB}{CA} = \frac{CE}{CD} \rightarrow \frac{12}{(x+2)} = \frac{4}{x}$ and got that $x = 1$. Am I incorrect? If yes, then what would be the proper approach to this problem?
$\endgroup$ 01 Answer
$\begingroup$You need to flip the smaller triangle to setup your ratio. That would setup a ratio of $\frac{CB}{CA}=\frac{CD}{CE}$ If you were to imagine that the drawing is to scale, you could think$\frac{\text{C to longer side}}{\text{C to shorter side}}=\frac{\text{C to longer side}}{\text{C to shorter side}}$
$$\frac{CB}{CA} = \frac{CD}{CE} \rightarrow \frac{12}{(x+2)} = \frac{x}{4}$$
$\endgroup$ 4
