Here we are given that the Alligator's tail length t varies directly as its body length b.
Using this given information and taking k as constant of proportionality, we get this equation :
[tex] t=kb [/tex].................(1)
Now we are given:
body length (b) = 4 feet
tail length (t) = 2.5 feet
plugging these values in equation (1) we have,
[tex] 2.5=k*4 [/tex]
from here we can calculate the value of k, dividing both sides by 4
k=2.5/4 = 0.625.............(2)
Now we have to find tail length of alligator if body length is 3.2 feet.
so plugging b=3.2 and k=0.625 in equation (1)
[tex] t=3.2 * 0.625 [/tex]
t= 2
So tail length is 2 feet when body length of alligator is 3.2 feet.
