189k views
5 votes
What is the length of CD? In this diagram, ΔABC ~ ΔEDC.

What is the length of CD? In this diagram, ΔABC ~ ΔEDC.-example-1

1 Answer

4 votes

Answer:

4

Explanation:

Knowing that the triangles are similar you know that AC is proportional to EC. Knowing that AC is 20 and EC is 5 we know that the sides of triangle EDC are 1/4th the size of those on ABC. Therefore, because BC and CD are proportional by that same ratio, we know that BC = 4CD, or 20-x = 4x by substitution. You can then add the x over from the left using the addition property of equality to give you 20 = 5x. You then use the division property of equality to get that x = 4. If CD is also equal to x then CD can be substituted in for x to get that the length of CD = 4

User Harry F
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.