Question

Here are two rectangles.

Answer 1

Answer:

$AB=9.5\ cm$

Step-by-step explanation:

step 1

Find the length side PQ

we know that

The area of rectangle PQRS is given by

$A=(PQ)(QR)$

$A=66\ cm^2$

so

$66=(PQ)(QR)$

substitute the value of QR

$66=(PQ)(12)$

solve for PQ

$PQ=66/12\\PQ=5.5\ cm$

step 2

Find the length side AB

we know that

The perimeter of rectangle ABCD is given by

$P=2(AB+BC)$

we have

$P=30\ cm\\BC=PQ=5.5\ cm$

substitute

$30=2(AB+5.5)$

solve for AB

$15=AB+5.5\\AB=15-5.5\\AB=9.5\ cm$