Question

The perimeter P of a square (measured in inches) is expanding in size at a constant rate of change of 4 inches per inch with respect to the square's side length s (measured in inches). If the length of the side of the square changes from:

a. 0 to 2.5 inches, how does the square's perimeter P change?
b. 1 to 3 inches, how does the square's perimeter P change?
c. Express the change in the square's perimeter P in terms of the change in the square's side length s.

Answer 1

a. 10 inches

b. 8 inches

c.
`(dP)/(ds) = 4`

Explanation:

a. At side 0, perimeter is 0*4 = 0 in. At side 2.5 inches, perimeter = 2.5*4 = 10 inches, a change of 10 - 0 = 10 inches

b. At side 1, perimeter is 1*4 = 4 inches. At side 3 inches, perimeter = 3*4 = 12 inches, a change of 12 - 4 = 8 inches.

c. We can express the change in the square's perimeter P in terms of the change in the square's side length s as

`(dP)/(ds) = 4`