Question

question 7 of 10 what is the length of cd? in this diagram, △abc ~ △edc.

Explanation:

Step1: Use property of similar triangles

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

Step2: Cross - multiply

Cross - multiplying the equation $\frac{21}{7}=\frac{20 - x}{x}$ gives $21x=7(20 - x)$.

Step3: Expand and solve for x

Expand the right - hand side: $21x = 140-7x$. Add $7x$ to both sides: $21x + 7x=140$, which simplifies to $28x = 140$. Divide both sides by 28: $x = 5$.

Answer:

A. 5