Question

1. triangle abc is similar to triangle dbe. ac:de is 3:2 and the length of ab is 42. what is the length of db? 21 14 28 16.8

Explanation:

Step1: Use similarity - ratio property

Since $\triangle ABC\sim\triangle DBE$, we have $\frac{AC}{DE}=\frac{AB}{DB}$. Given $\frac{AC}{DE}=\frac{3}{2}$ and $AB = 42$. Let $DB=x$. Then $\frac{3}{2}=\frac{42}{x}$.

Step2: Cross - multiply

Cross - multiplying the equation $\frac{3}{2}=\frac{42}{x}$ gives $3x=42\times2$.

Step3: Solve for $x$

$3x = 84$, so $x=\frac{84}{3}=28$.

Answer:

28