Giben the triangles:
ABC and PQR
Thiangle PQR is a reduction of triangle ABC, this means that the sides of triangle ABC were divided by a reduction factor to determine the side lengths of triangle PQR.
Using the lengths of sides AB and its correspoding side PQ you can calculate the used reduction factor k following the formula:
[tex]PQ=\frac{AB}{k}[/tex]
Using this relationship you can determine the value of the reduction factor
[tex]\begin{gathered} PQ=\frac{AB}{k} \\ k\cdot PQ=AB \\ k=\frac{AB}{PQ} \\ k=\frac{20}{5} \\ k=4 \end{gathered}[/tex]
The reduction factor is k=4
Now that we have determined the factor, we can calculate the length of PR as:
[tex]\begin{gathered} PR=\frac{AC}{k} \\ x=\frac{24}{4} \\ x=6 \end{gathered}[/tex]
The length of PR=6, so the correct option is C.
