Final answer:
By dividing the area of the rectangle by its length, we determined that the width is 2 meters. Setting that equal to 2y^4 and solving for y, we find that y must be 1, which does not match the provided options. There might be a typo in the question or additional information is needed.
Step-by-step explanation:
To find the value of y, we will use the formula for the area of a rectangle, which is given as the product of its length and width. Given the area as 60y^4 square meters and the length as 30 meters, we can set up the equation:
30 × width = 60y^4
To find the width, we divide both sides by 30:
width = × = 2y^4 meters
Since the width of a rectangle cannot be in terms of y, it is implied that width = 2 meters. Now we can set up the equation:
2 = 2y^4
Dividing both sides by 2 gives us:
1 = y^4
Taking the fourth root of both sides, we find:
y = 1
However, in the given options, the smallest value for y is 2. So since y must be greater than or equal to 1 and our result is y = 1, we will not be using the smallest given value. There seems to be a contradiction between the specified options and the result obtained from our calculation. The question might either have a typo or more information is needed to match the given options.