Question

if triangle ABC is approximately equal to triangle DEC, ED=4y+2, and AB=6y-4,what is the length of AB?

Answer 1

Since both triangles are aproximately equal, we can say that:

$\begin{gathered} ED=AB \\ \rightarrow4y+2=6y-4 \end{gathered}$

Solving for y :

$\begin{gathered} 4y+2=6y-4 \\ \rightarrow2+4=6y-4y \\ \rightarrow8=2y\rightarrow\frac{8}{2}=y \\ \\ \Rightarrow y=4 \end{gathered}$

Substituting in the expression for AB,

$\begin{gathered} AB=6y-4 \\ \rightarrow AB=6(4)-4 \\ \rightarrow AB=20 \end{gathered}$

Thereby, AB = 20