Question

given $\triangle abesim\triangle dce$ and $overline{bc}$ intersects $overline{ad}$ at $e$, what is the value of $y$?

Explanation:

Step1: Use property of similar triangles

If $\triangle ABE\sim\triangle DCE$, then the ratios of corresponding - sides are equal. That is, $\frac{AE}{DE}=\frac{BE}{CE}$. Given $AE = 24$, $DE = 4$, and $CE = 4$. Let $BE=y$.
So, $\frac{24}{4}=\frac{y}{4}$.

Step2: Solve the proportion for $y$

Cross - multiply the proportion $\frac{24}{4}=\frac{y}{4}$ to get $24\times4 = 4y$. Then divide both sides of the equation $96 = 4y$ by 4. We have $y=\frac{96}{4}=24$.

Answer:

24