Answer:
5 1/3 square feet
Explanation:
You want the area of a rectangle whose width is 2 ft, if it is similar to one with a perimeter of 14 ft and a length of 4 ft.
Width
The perimeter can be used to find the width of the larger rectangle.
P = 2(L +W)
14 = 2(4 +W)
7 = 4 +W
3 = W
The width of the outer rectangle is 3 ft.
Scale factor
The width of the inner rectangle is 2 ft, so is 2/3 of the width of the outer rectangle.
The length of the shaded rectangle will be 2/3 of the length of the outer rectangle, so is ...
length = (2/3)(4 ft) = 8/3 ft
Area
The area of the shaded rectangle is ...
A = LW
A = (8/3 ft)(2 ft) = 16/3 ft² = 5 1/3 ft²
The shaded area is 5 1/3 square feet.
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Additional comment
You can also figure the area of the outer rectangle: (3 ft)(4 ft) = 12 ft². Then you can use the scale factor to find the shaded area:
shaded area = (12 ft²)(2/3)² = 48/9 ft² = 16/3 ft² = 5 1/3 ft²
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