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klio [65]
2 years ago
5

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

Mathematics
2 answers:
aliina [53]2 years ago
6 0

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

LenKa [72]2 years ago
5 0

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

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