A rectangle has a length of 11 inches and a width of 7 inches whose sides are changing. The length is decreasing by 6 in/sec and the width is shrinking at 5 in/sec.

Question

What is the rate of change of the perimeter ?

Answer 1

Using the area of rectangle to find the formula for the area and the perimeter shows us..

A = L*W

P = 2L + 2W

dA/dt = L * dW/dt. + dL/dt * W

dP/dt = 2 * ( dL/dt + dW/dt )

We are given the following information...

L = 11 in

W = 7 in

dL/dt = -6 in/sec ( decreasing so the sign is negative )

dW/dt = -5 in/sec ( decreasing so the sign is negative )

dP/dt = 2 * (-6 + -5) in/sec = -22 in/sec