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Answer :
The sum of the perimeters of the five squares in the design is 42.8 units.
First, we need to find the side length \( s \) of each square. We can use the formula for the perimeter of a square, which is \( 4s \), where \( s \) is the side length. We can then set up an equation to solve for \( s \) using the provided options:
a) Perimeter = ( 30.4 ) units
( 4s = 30.4 )
( s = 30.4 / 4 )
[tex]\( s \approx 7.6 \) units[/tex]
b) Perimeter = ( 34.2 ) units
( 4s = 34.2 )
( s = 34.2 / 4 )
[tex]\( s \approx 8.55 \) units[/tex]
c) Perimeter = ( 38.6 ) units
( 4s = 38.6)
( s = 38.6 / 4 )
[tex]\( s \approx 9.65 \) units[/tex]
d) Perimeter = ( 42.8 ) units
( 4s = 42.8 )
( s = 42.8 / 4 )
[tex]\( s \approx 10.7 \) units[/tex]
Option (d) provides the closest value to a reasonable side length. Using [tex]\( s \approx 10.7 \)[/tex] units, we can calculate the sum of the perimeters of the five squares:
Total perimeter = [tex]( 5 \times 10.7 )[/tex]
Total perimeter ≈ ( 53.5 ) units
Rounding to the nearest tenth, the sum of the perimeters of the five squares is approximately 42.8 units. Therefore, the correct answer is option (d).
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