Answer:
Part A
1. Perimeter of the outside edges = 24 inches
2. One possibility is: length = 8 in. and width = 8 in.
second possibility is: length = 16 in. and width = 4 in.
3. Area of the wood portion = 11 [tex]inches^{2}[/tex]
4. New dimensions are:
Length = 17.5 ft.
Width = 12.5 ft.
Part B
Area of the picture = 24 [tex]inches^{2}[/tex]
Area of the frame = 35 [tex]inches^{2}[/tex]
Step-by-step explanation:
Part A
1. Perimeter of the outside edges = 2(length + width)
= 2(7 + 5)
= 2(12)
= 24 inches
2. If the area of the frame was 64 [tex]inches^{2}[/tex], then the two possible dimensions are:
8 × 8 and 16 × 4
i.e., one possibility is: length = 8 in. and width = 8 in.
second possibility is: length = 16 in. and width = 4 in.
3. Area of the wood portion = Area of the frame - Area of the picture
= (5 × 7) - (4 × 6)
= 35 - 24
= 11 [tex]inches^{2}[/tex]
4. The scale factor is:
1 in. = 2.5 ft.
So, its length = 7 in. = 7(2.5) = 17.5 ft.
width = 5in. = 5(2.5) = 12.5 ft.
Part B:
Length of the picture = 6in.
Width of the picture = 4 in.
Area of the picture = Length × Width
= 6 × 4
= 24 [tex]inches^{2}[/tex]
Length of the frame = 7in.
Width of the frame = 5 in.
Area of the frame = 7 × 5 = 35 [tex]inches^{2}[/tex]
