For the given rectangles, [tex]f=4[/tex] cm and [tex]g = 6[/tex] cm.
Step-by-step explanation:
Step 1:
The area of a rectangle is calculated by multiplying its length with its width. Both the rectangles APQD and PBCQ have the same width.
The second rectangle PBCQ has a length of 9 cm. Its area is determined by subtracting the area of APQD from the area of ABCD.
The area of the rectangle PQBC [tex]= 60 - 24 = 36[/tex] [tex]cm^{2}[/tex].
Step 2:
The length of rectangle PBCQ is 9 cm and the area is 36 [tex]cm^{2}[/tex] so the width can be determined.
[tex]Width = \frac{area}{length} = \frac{36}{9} = 4[/tex] cm. So [tex]f=4[/tex] cm.
Step 3:
The width of the rectangle APQD is also 4cm.
The width of the rectangle APQD is 4 cm and the area is 24 [tex]cm^{2}[/tex].
[tex]length = \frac{area}{width} = \frac{24}{4} = 6[/tex] cm. So [tex]g = 6[/tex] cm.
