Question

If the sides of a square are decreasing at the rate of \( 1.5 \, \mathrm{cm/s} \), the rate of decrease of its perimeter is:

• A. \( 1.5 \, \mathrm{cm/s} \)
• B. \( 6 \, \mathrm{cm/s} \)
• C. \( 3 \, \mathrm{cm/s} \)
• D. \( 2.25 \, \mathrm{cm/s} \)

Hint:

Perimeter-related rates are proportional to the rate of change of the side length.

Answer 1

The Correct Option is B

The perimeter \( P \) of a square with side length \( s \) is: \[ P = 4s. \] The rate of change of the perimeter is: \[ \frac{dP}{dt} = 4 \cdot \frac{ds}{dt}. \] Substitute \( \frac{ds}{dt} = -1.5 \, \mathrm{cm/s} \): \[ \frac{dP}{dt} = 4 \cdot (-1.5) = -6 \, \mathrm{cm/s}. \] Thus, the rate of decrease of the perimeter is \( 6 \, \mathrm{cm/s} \).
Final Answer: \( \boxed{6 \, \mathrm{cm/s}} \)