What expression represents the value of v? v equals the square root of A A. quantity z times y end quantity
B. v equals the square root of quantity w times z end quantity
C. v equals the square root of quantity w times the sum of w plus z end quantity
D. v equals the square root of quantity z times the sum of w plus z end quantity

D. v equals the square root of quantity z times the sum of w plus z end quantity

Step-by-step explanation:

We will use pythagoras theorem to solve this question. According to ΔABD, side AB is the hypotenuse of the triangle while AD and BD are the opposite and adjacent sides.

From ΔABD, v² = z² + y² ... 1

Also from ΔABC, side AC is the hypotenuse, AB and BC are the opposite and the adjacent side. Since AC = w+z, AB =  v and AC = x, then;

AC² = AB²+BC²

(w+z)² = v²+x²

v² = (w+z)² - x² ... 2

Also, from ΔBCD, x² = y²+w²... 3

Substituting equation 3 into 2 will give;

v² = (w+z)² - x²

v² = (w+z)² - (y²+w²) ... 4

Equating 1 and 4

z²+y² = (w+z)² - (y²+w²)

z²+y² =w²+z²+2wz - (y²+w²)

z²+y² =w²+z²+2wz - y² - w²

z²+y² = z²+2wz - y²

2y² = 2wz

y² = wz ... 5

From equation 1; v² = z² + y²

substituting eqn 5 into 1;

v² = z²+wz

v = √z(w+z)

Hence the correct expression of v in words is 'v equals the square root of quantity z times the sum of w plus z end quantity'

answer: do we write it

step-by-step explanation: