Question

question 8 of 10
what is the length of (overline{cd})? in this diagram, (\triangle abcsim\triangle edc).
a. 5
b. 3
c. 6
d. 4

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle EDC\), the ratios of corresponding sides are equal. That is \(\frac{AC}{EC}=\frac{BC}{DC}\).
Given \(AC = 21\), \(EC=7\), \(BC = 20 - x\), \(DC=x\). So \(\frac{21}{7}=\frac{20 - x}{x}\).

Step2: Solve the proportion

Simplify \(\frac{21}{7}=\frac{20 - x}{x}\) to \(3=\frac{20 - x}{x}\).
Cross - multiply: \(3x=20 - x\).
Add \(x\) to both sides: \(3x+x=20\), \(4x = 20\).
Divide both sides by \(4\): \(x = 5\).

Answer:

A. 5