Answer:
[tex]AB=9.5\ cm[/tex]
Step-by-step explanation:
step 1
Find the length side PQ
we know that
The area of rectangle PQRS is given by
[tex]A=(PQ)(QR)[/tex]
[tex]A=66\ cm^2[/tex]
so
[tex]66=(PQ)(QR)[/tex]
substitute the value of QR
[tex]66=(PQ)(12)[/tex]
solve for PQ
[tex]PQ=66/12\\PQ=5.5\ cm[/tex]
step 2
Find the length side AB
we know that
The perimeter of rectangle ABCD is given by
[tex]P=2(AB+BC)[/tex]
we have
[tex]P=30\ cm\\BC=PQ=5.5\ cm[/tex]
substitute
[tex]30=2(AB+5.5)[/tex]
solve for AB
[tex]15=AB+5.5\\AB=15-5.5\\AB=9.5\ cm[/tex]
