Respuesta :

sqdancefan

Answer:

  x = 3

Step-by-step explanation:

The angle bisector creates proportional segments:

  8x/(10x -2) = (5x +3)/(7x) . . . . left side segments have the same ratio as right side segments

  56x^2 = (10x -2)(5x +3) . . . . . multiply by 7x(10x -2)

  56x^2 = 50x^2 +20x -6 . . . . eliminate parentheses

  6x^2 -20x +6 = 0 . . . . . . . . . subtract the right side

  3x^2 -10x +3 = 0 . . . . . . . . . . divide by 2

  (3x -1)(x -3) = 0 . . . . . . . . . . . . factor

Solutions are x = 1/3, x = 3

_____

Check

For x = 1/3, side lengths are ...

  Left side: 8/3, 10/3 -2 = 4/3

  Right side: 5/3 +3 = 14/3, 7/3

  Triangle sides are 4/3, 22/3, 7/3. Short sides are too short to make a triangle This is an extraneous solution.

For x = 3, side lengths are ...

  Left side: 8·3 = 24, 10·3 -2 = 28

  Right side: 5·3 +3 = 18, 7·3 = 21

  Triangle sides are ... 28, 42, 21

MrRoyal

The triangle is an illustration of similar triangles

The values of x are 1/3 and 3

To solve for x, we make use of the following ratio

[tex]8x: 10x -2 = 5x +3: 7x[/tex]

Express as fraction

[tex]\frac{8x}{10x -2} = \frac{5x +3}{7x}[/tex]

Cross multiply

[tex]56x^2 = 50x^2 +20x -6[/tex]

Evaluate the like terms

[tex]6x^2 - 20x + 6 = 0[/tex]

Divide through by 2

[tex]3x^2 - 10x + 3 = 0[/tex]

Factorize

[tex](3x -1)(x -3) = 0[/tex]

Solve for x

x = 1/3 or x = 3

Hence, the values of x are 1/3 and 3

Read more about similar triangles at:

https://brainly.com/question/14285697

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