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?

Explanation:

Step1: Use the property of similar - triangles

Since $\triangle ABC\sim\triangle DBE$, we have the proportion $\frac{AC}{DE}=\frac{AB}{DB}$.

Step2: Substitute the given values

We know that $\frac{AC}{DE} = 3.2$ and $AB = 42$. Let $DB=x$. Then $3.2=\frac{42}{x}$.

Step3: Solve for $x$

Cross - multiply to get $3.2x = 42$. Then $x=\frac{42}{3.2}=\frac{420}{32}=\frac{105}{8}=13.125$.

Answer:

$13.125$