SOLUTION:
Step 1:
In this question, we are given the following:
ABC is similar to DEF.
The measure of AB = 6,
the measure of DE = 18,
the measure of BC = 12,
and the measure of DF = 15.
Find the measures of AC and EF.
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Since\text{ ABC }\cong\text{ DEF} \\ This\text{ means that:} \\ \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF} \end{gathered}[/tex][tex]and\text{ AB = 6, DE = 18, BC = 12, DF = 15}[/tex][tex]\frac{}{}\frac{6}{18}=\frac{12}{EF}=\frac{AC}{15}[/tex][tex]\begin{gathered} cross-multiply,\text{ we have that:} \\ \text{6 }\times\text{ EF =18 }\times\text{ 12} \\ Divide\text{ both sides by 6, we have that:} \\ EF\text{ =}\frac{18\times12}{6}=\frac{216}{6}=\text{ 36} \\ Hence,\text{ EF = 36} \end{gathered}[/tex][tex]\begin{gathered} \frac{6}{18}=\frac{AC}{15} \\ cross-multiply\text{ we have that:} \\ 6\times15\text{ = AC }\times18 \\ Divide\text{ both sides by 18, we have that:} \\ AC\text{ =}\frac{6\text{ }\times15}{18}=\frac{90}{18}=\text{ 5} \\ Hence,\text{ AC = 5} \end{gathered}[/tex]
