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'

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

answer: b

step-by-step explanation: