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Sagot :

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].

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