Question

two similar triangles, △abc and △jkl are shown. what is the length of side jl?

Explanation:

Step1: Find the scale - factor

Since the two triangles $\triangle ABC$ and $\triangle JKL$ are similar, the ratio of corresponding sides is the same. Let's find the scale - factor using the known corresponding sides. The ratio of side $AC$ to side $KL$ is $\frac{AC}{KL}=\frac{2.5}{15}=\frac{1}{6}$.

Step2: Calculate the length of side $JL$

We know that side $AB$ corresponds to side $JL$. Let the length of side $JL$ be $x$. Using the scale - factor, we have $\frac{AB}{JL}=\frac{1}{6}$. Given $AB = 3.5$, we can write the equation $\frac{3.5}{x}=\frac{1}{6}$. Cross - multiplying gives us $x=3.5\times6 = 21$.

Answer:

21