Question

Determine the length of BC . ANSWERS: A) 12.25 units B) 24.71 units C) 19.00 units D) 5.57 units

Answer 1

A) 12.25 units

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