# Analyze and answer: The perimeter of a rectangle is a function of its length. If the length is 4 cm.,the perimeter is 20 cm. If the length is 8 cm., the perimeter is 28 cm. What equation will represent this function? At what length will the perimeter be 100 cm?

1
by elmerdiaz

2014-10-06T23:30:56+08:00
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