A square sheet of metal is heated so that its side length grows over time. At t=10 s the side length is 2.0 ft and is increasing at a rate of 0.25 ft s⁻¹.
(a) Calculate the instantaneous rate of change of the area of the sheet at t=10 s. State units clearly.
(b) Determine the instantaneous rate of change of the perimeter of the sheet at the same instant. Provide units.
(c) Compare the numerical results from parts (a) and (b). Explain which geometric quantity—area or perimeter—is changing more rapidly in relative terms at t=10 s. Justify your conclusion using appropriate ratios or percentages.