An alligator’s tail length, T, varies directly as its body length, B. An alligator with a body length of 4.5 feet has a tail length of 2.5 feet. What is the tail length of an alligator whose body length is 5.4 feet?
4.5/2.5 = 5.4/x
Cross multiply and solve for x.
To solve this problem, we can use the concept of direct variation, which states that two quantities are directly proportional if they can be expressed as y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation.
In this case, the tail length (T) is directly proportional to the body length (B). So, we can write the equation as T = kB.
Given that an alligator with a body length of 4.5 feet has a tail length of 2.5 feet, we can substitute these values into the equation to find the constant of variation (k).
2.5 = k(4.5)
To find k, divide both sides of the equation by 4.5:
k = 2.5/4.5
k ≈ 0.5556
Now that we have the value of k, we can use it to find the tail length (T) for an alligator with a body length of 5.4 feet. Substituting the values into the equation:
T = 0.5556(5.4)
T ≈ 2.9992
Therefore, the tail length of an alligator with a body length of 5.4 feet is approximately 2.9992 feet.