Question

What is the length of CD in this diagram ABC ~ EDC

Answer 1

We are given that:

ABC ~ EDC

So equating ratio of equal sides:

$\frac{BC}{CD} = \frac{AC}{CE}$

$\frac{20-x}{x} = \frac{21}{7}$

$20-x =3x$

$20 =3x+x$

$20 =4x$

dividing both sides by 4,

x=5

Answer is length of CD is x which is 5. Option C

Answer 2

Answer:

C. 5

Step-by-step explanation:

Given the two triangles are similar, then its sides are proportional. In consequence the following relation must be satisfied:

BC/AC =  CD/CE

Replacing with the given values and solving for x, we get

(20 - x)/21 = x/7

(20 - x) = 21*x/7

20 - x = 3*x

20 = 3*x + x

20 = 4*x

20/4 = x

5 = x