Question

1. if the triangles are similar, find the length of side f.

e = \frac{1}{3} mi, g = \frac{1}{4} mi, j = 2 mi, k = \frac{5}{2} mi\
\bigcirc \\ \frac{5}{16}mi\
\bigcirc \\ \frac{4}{15}mi\
\bigcirc \\ \frac{5}{12} mi\
\bigcirc \\ 3\frac{1}{3}mi

Explanation:

Step1: Set up similarity proportion

$\frac{e}{j} = \frac{f}{k}$

Step2: Substitute given values

$\frac{\frac{1}{3}}{2} = \frac{f}{\frac{5}{2}}$

Step3: Simplify left-hand side

$\frac{1}{3} \times \frac{1}{2} = \frac{f}{\frac{5}{2}}$
$\frac{1}{6} = \frac{f}{\frac{5}{2}}$

Step4: Solve for $f$

$f = \frac{1}{6} \times \frac{5}{2}$
$f = \frac{5}{12}$

Answer:

$\boldsymbol{\frac{5}{12}}$ mi (Option C: $\frac{5}{12}$ mi)