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Irina18 [472]
3 years ago
13

If AACD ~ AABE, find the value of x.

Mathematics
1 answer:
Anastaziya [24]3 years ago
4 0

9514 1404 393

Answer:

  x = 16

Step-by-step explanation:

Corresponding sides are proportional.

  BE/CD = AE/AD

  20/(3x+8) = (x-1)/(x-1+27)

  20(x+26) = (3x+8)(x -1)

In standard form, this is ...

  3x^2 -15x -528 = 0

  x^2 -5x -176 = 0 . . . . . . divide by 3

  (x -16)(x +11) = 0 . . . . . . . factor

  x = 16

__

This is the positive value that makes the product zero. x=-11 will also make the product 0, but gives negative segment lengths in the geometry. It is an extraneous solution.

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