Question

Here are two rectangles.

QR = 12 cm
BC = PQ
12 cm
The perimeter of ABCD is 30 cm.
The area of PQRS is 66 cm2
Find the length of AB. (Your final line must say AB = ...)​

Answer 1

AB= 9.5 cm

Explanation:

Answer 2

`AB=9.5\ cm`

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`