Question

what is the length of $overline{cd}$? in this diagram, $\triangle abcsim\triangle edc.$

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 the right - hand side

Expand $7(20 - x)$ to get $21x = 140-7x$.

Step4: Add $7x$ to both sides

Adding $7x$ to both sides of the equation $21x = 140-7x$ gives $21x + 7x=140$, which simplifies to $28x = 140$.

Step5: Solve for $x$

Dividing both sides of $28x = 140$ by 28, we have $x=\frac{140}{28}=5$.

Answer:

B. 5