Question

Triangle ABC with segment BD where point D is between points C and A, BC equals x, BD equals y, CD equals w, DA equals z, and BA equals v
What expression represents the value of x?


x equals the square root of quantity w times the sum of w plus z end quantity

x equals the square root of quantity z times the sum of w plus z end quantity

x equals the square root of quantity w times y end quantity

x equals the square root of quantity w times z end quantity

Answer 1

Answer:

The correct option is

x equals the square root of w times the sum of w plus z end quantity

Step-by-step explanation:

The parameters given are

ABC = Right triangle, with ∠B = 90° and CA = Hypotenuse = CD + DA

∴ CA = w + z

BA = v

Hence;

x² = (w + z)² - v²

Where:

v² = z² + y²

∴ x² = (w + z)² - (z² + y²)

x² = w² + 2·w·z + z² - z² - y²

x² = w² + 2·w·z - y²

Where:

y² = x² - w²

We have;

x² = w² + 2·w·z - (x² - w²)

x² = w² + 2·w·z - x² + w²

Which gives;

2·x² = 2·w² + 2·w·z

Removing the common factors, we have;

x² = w² + w·z

$\therefore x = \sqrt{w^2 + w \times z} = \sqrt{w \times(w + z)}$

The correct option is x equals the square root of w times the sum of w plus z end quantity.