The equation for the perimeter is [tex]P = 10n+8.[/tex]
Step-by-step explanation:
Step 1:
The perimeter of a parallelogram is twice the sum of its base length and side length.
First, we determine the perimeters of each of the given parallelograms.
If n is the number of parallelograms in the figure, then
When n = 1, the perimeter [tex]= 2(5+4) = 2(9) = 18.[/tex]
When n = 2, the perimeter [tex]= 2 (10+4) = 2 (14) = 28.[/tex]
When n = 3, the perimeter [tex]= 2(15+4) = 2(19) = 38.[/tex]
Step 2:
So when we substitute the values of n in the given options we get the following values. The perimeter of the first figure is 18 units.
Option 1; [tex]P=10n+4,[/tex] when n = 1, [tex]P= 10(1)+ 4 = 14,[/tex] [tex]14 \neq 18.[/tex]
Option 2; [tex]P=4n+10,[/tex] when n = 1, [tex]P= 4(1)+ 10 = 14,[/tex] [tex]14 \neq 18.[/tex]
Option 3; [tex]P=4n+5,[/tex] when n = 1, [tex]P= 4(1)+ 5 = 9,[/tex] [tex]9 \neq 18.[/tex]
Option 4; [tex]P=10n+8,[/tex] when n = 1, [tex]P= 10(1)+ 8 = 18.[/tex]
Only option 4 satisfies the given equation. So [tex]P = 10n+8.[/tex]
