Question

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if $\triangle adesim\triangle acb$, $\frac{ad}{ac}=\frac{2}{3}$, and $de = 10$, then $bc=square$.

Explanation:

Step1: Recall property of similar triangles

For similar triangles $\triangle ADE\sim\triangle ACB$, the ratios of corresponding - sides are equal. That is $\frac{AD}{AC}=\frac{DE}{BC}$.

Step2: Substitute given values

We know that $\frac{AD}{AC}=\frac{2}{3}$ and $DE = 10$. Substituting into $\frac{AD}{AC}=\frac{DE}{BC}$, we get $\frac{2}{3}=\frac{10}{BC}$.

Step3: Solve for $BC$

Cross - multiply: $2\times BC=3\times10$, so $2BC = 30$. Then $BC=\frac{30}{2}=15$.

Answer:

15