Question

in the figure to the right, $delta abc$ and $delta ade$ are similar. find the length of $overline{ec}$. the length of $overline{ec}$ is $square$. (simplify your answer.)

Explanation:

Step1: Use similarity - side ratio

Since $\triangle ABC$ and $\triangle ADE$ are similar, the ratios of corresponding sides are equal. That is, $\frac{BC}{DE}=\frac{AC}{AE}$. We know $BC = 1$, $DE=6$, and $AE = 7$. Let $AC=x$, then $EC=7 - x$. So $\frac{1}{6}=\frac{x}{7}$.

Step2: Solve for $x$

Cross - multiply the equation $\frac{1}{6}=\frac{x}{7}$ to get $6x = 7$, then $x=\frac{7}{6}$.

Step3: Calculate $EC$

$EC=AE - AC$. Substitute $AE = 7$ and $AC=\frac{7}{6}$ into the formula. $EC=7-\frac{7}{6}=\frac{42 - 7}{6}=\frac{35}{6}$.

Answer:

$\frac{35}{6}$