Question

ΔABC was dilated from point A to get ΔADE. Find the length of AD given a scale factor of 4.

Answer 1

Since triangle ADE is similar to triangle ABC and the scale factor is 2, the following relation must be fulfilled:

`(AD)/(AB)=4`

The, by substituting the given information, we have

`\begin{gathered} (6x-8)/(x+2)=4 \\ \end{gathered}`

By multiplying both sides by x+2, we get

`6x-8=4(x+2)`

which gives

`6x-8=4x+8`

Then, by subtracting 4x to both sides, we have

`2x-8=8`

and by adding 8 to both sides, we obtain

`2x=16`

then, x is given by

`x=(16)/(2)=8`

Then, by substitutn