Question

in the figure to the right, △abc and △ade are similar. find the length of ec. the length of ec is (simplify your answer.)

Explanation:

Step1: Use similarity of triangles property

Since $\triangle ABC$ and $\triangle ADE$ are similar, the ratios of corresponding sides are equal. That is, $\frac{AC}{AE}=\frac{AB}{AD}$. Let $EC = x$, then $AC=9 - x$. We know $AB = 1$, $AD=1 + 10=11$, and $AE = 9$. So, $\frac{9 - x}{9}=\frac{1}{11}$.

Step2: Cross - multiply

Cross - multiplying the equation $\frac{9 - x}{9}=\frac{1}{11}$ gives us $11(9 - x)=9\times1$.

Step3: Expand the left - hand side

Expanding $11(9 - x)$ we get $99-11x = 9$.

Step4: Solve for $x$

First, subtract 99 from both sides: $-11x=9 - 99=-90$. Then divide both sides by - 11, so $x=\frac{90}{11}$.

Answer:

$\frac{90}{11}$