Respuesta :

Answer:

A) 12.25 units

Step-by-step explanation:

From Pythagorean theorem:

  • AB² + BC² = 25²
  • 6² + BD² =  BC²
  • 19² + BD² = AB²

Defining:

  • x = AB²
  • y = BC²
  • z = BD²

The system of equations is:

x + y = 625   (eq. 1)

36 + z = y     (eq. 2)

361 + z = x    (eq. 3)

Replacing equation 3 into 1:

361 + z + y = 625

From equation 2:

z = y - 36

Replacing it into equation 1:

361 + y - 36 + y = 625

2y = 625 + 36 - 361

y = 300/2

y = 150

Finally:

BC = √y

BC = √150

BC = 12.25 units

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