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:

$\frac{AD}{AB}=4$

The, by substituting the given information, we have

$\begin{gathered} \frac{6x-8}{x+2}=4 \\ \end{gathered}$

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

$x=\frac{16}{2}=8$

Then, by substitutn