Answer:
7
Step-by-step explanation:
Similarity of Triangles
When two triangles are similar, it means that
- all of their angles
- all of their side lengths
correlate, spatially.
It could be thought of as two triangles where one is the scaled-up/down version of the other.
The ratio between all of their corresponding side lengths is the same.
[tex]\hrulefill[/tex]
Solving the Problem
We're told that ABC and DEF are similar, which means that
- line AB and DE correlate
- lines BC and EF correlate
- lines AC and DF correlate
or
[tex]\dfrac{AB}{DE} =\dfrac{BC}{EF} =\dfrac{AC}{DF}[/tex].
We can substitute the values seen in the image into that equation to find x!
[tex]\dfrac{30}{25} =\dfrac{12}{10} =\dfrac{2x+4}{x+8}[/tex]
Since [tex]\dfrac{30}{25}=\dfrac{12}{10}[/tex] we can use either one to equate to the rightmost ratio.
[tex]\dfrac{12}{10} =\dfrac{2x+4}{x+8}[/tex]
[tex]12x+96=20x+40[/tex] (cross multiply)
[tex]96=20x-12x+40[/tex]
[tex]96-40=20x-12x[/tex]
[tex]56=8x[/tex]
[tex]\boxed{7=x}[/tex].
