Respuesta :

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[tex] \dfrac{4x - 1}{x + 5} = \dfrac{60}{24} [/tex]

[tex] \dfrac{4x - 1}{x + 5} = \dfrac{5}{2} [/tex]

[tex] 5(x + 5) = 2(4x - 1) [/tex]

[tex] 5x + 25 = 8x - 2 [/tex]

[tex] -3x = -27 [/tex]

[tex] x = 9 [/tex]

The value of x given that ∆GFE is congruent to ∆CBE is; x = 9

Similar Triangles

We are given that;

∆GFE is congruent to ∆CBE.

Now, the corresponding sides of both triangles are;

  • FE is congruent to BE
  • GE is congruent to CE
  • BC is congruent to FG

We see that;

FE = 4x - 1

BE = x + 5

CE = 24

GE = 60

Thus,by similar triangles, we have;

(4x - 1)/(x + 5) = 60/24

>> (4x - 1)/(x + 5) = 5/2

>> 2(4x - 1) = 5(x + 5)

>> 8x - 2 = 5x + 25

>> 8x - 5x = 25 + 2

3x = 27

x = 27/3

x = 9

Read more about Similar triangles at; https://brainly.com/question/14285697

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