Respuesta :

If the shapes are similar, the correspondent sides are in proportion:

[tex]AB\div DE = BC \div EF[/tex]

Let's plug the values and solve for x:

[tex]5x \div 5 = 4 \div x \iff \dfrac{5x}{5}=\dfrac{4}{x}\iff x = \dfrac{4}{x}[/tex]

Multiply both sides by x to get

[tex]x^2=4 \iff x=\pm2[/tex]

The only feasible solution, though, is [tex]x=2[/tex], because it wouldn't make sense to have negative lengths.

akposevictor

The value of x in the similar polygons in the given diagram is: B. x = 2.

What are the Sides of Similar Polygons?

Similar polygons have the same shape but different size, thus, the length of their corresponding sides are proportional together and have equal ratio.

In essence, we will have the following ratio:

5x/5 = 4/x

(x)(5x) = (4)(5)

5x² = 20

5x²/5 = 20/5

x² = 4

x = √4

x = 2 (option B)

Learn more about similar polygons on:

https://brainly.com/question/2264759

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