Final answer:
The width of a rectangle with a fixed area varies inversely with its length. The width is 1.8 inches when the length is 40 inches, based on the given data of a width of 4 inches when the length is 18 inches.
Step-by-step explanation:
The width y of a rectangle with a fixed area varies inversely with its length x. This means that as the length increases, the width decreases to maintain the same area, and vice versa. The relationship between the width and the length can be expressed as y = k/x, where k is the constant of variation.
Given that the width is 4 inches when the length is 18 inches, we can find the constant of variation by multiplying these two values: k = 4 inches × 18 inches = 72 in² (the area of the rectangle).
Now, to find the width when the length is 40 inches, we use the same relationship: y = k/x.
Here, y = 72 in² / 40 inches.
By calculating this, we get y = 1.8 inches, which is the width of the rectangle when the length is 40 inches.