Answer:
[tex]PQ=4\ cm[/tex]
Step-by-step explanation:
see the attached figure with the letter D to better understand the problem
we know that
The segment side AD is the height of triangle ABC
so
Triangles PBQ and ABD are similar by AA Similarity Theorem
The area of triangle ABC is equal to
[tex]A=\frac{1}{2}(BC)(AD)[/tex]
we have
[tex]A=48\ cm^2\\BC=12\ cm[/tex]
substitute
[tex]48=\frac{1}{2}(12)(AD)[/tex]
[tex]AD=8\ cm[/tex]
Remember that
If two triangles are similar then the ratio of its corresponding sides is proportional
so
[tex]\frac{BP}{AB}=\frac{PQ}{AD}[/tex]
substitute the given values
[tex]\frac{BP}{2BP}=\frac{PQ}{8}[/tex]
[tex]\frac{1}{2}=\frac{PQ}{8}[/tex]
[tex]PQ=4\ cm[/tex]
