Since the perimeter is a function of length then we'll have it as the function

P(x) = ax + b; where x is the length

since you're given that when the length is 4, the perimeter is 20 and when length is 8, perimeter is 28 then you will have the equations as

P(x) =ax + b

20 = a(4) + b ----equation 1

28 = 8a + b ----equation 2

from equation 1

20 = 4a + b

b = 20 - 4a -----equation 3

substitute equation 3 to equation 2

28 = 8a + b

28 = 8a + (20 - 4a)

8a - 4a = 28 - 20

4a = 8

a = 2

substitute this to equation 3

b = 20 - 4a

b = 20 - 4(2)

b = 12

since we already have the values of a and b then we can now substitute it to the main equation P(x) = ax + b

P(x) = ax + b

__P(x) = 2x + 12__

to find the length for the given perimeter which is 100, we then use the acquired equation

P(x) = 2x + 12

100 = 2x + 12

2x = 100 -12

2x = 88

**x = 44**