Question

How to find values of X and Y using scale factors?

Answer 1

According to the similarity of triangles we can conclude that two triangles are similar if

$A=K\cdot B$

in which A is the measure of one side of the initial triangle, B is the corresponding side into the other triangle amd k is the scale factor.

Using this

$\begin{gathered} AB=k\cdot(DE) \\ 6=k\cdot21 \\ k=\frac{6}{21} \\ k=\frac{2}{7} \end{gathered}$

using k find the values of x and y

$\begin{gathered} AC=k\cdot DC \\ x=(\frac{2}{7})\cdot(28) \\ x=2\cdot4 \\ x=8 \end{gathered}$$\begin{gathered} BC=k\cdot EC \\ 10=\frac{2}{7}\cdot y \\ y=10\cdot\frac{7}{2} \\ y=35 \end{gathered}$