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05-07-2024
Mathematics

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Answer choices are below the question. Thanks!

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zarahaider4211 zarahaider4211 · Answer 1 · 2024-07-05T13:21:09-04:00

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].