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=(6)/(21) \\ k=(2)/(7) \end{gathered}`

using k find the values of x and y

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