The rate of change of the perimeter of a rectangle is 4 in/sec.
What is the perimeter of a rectangle?
The whole length of the outline is referred to as the perimeter of a two-dimensional shape. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter. The rectangle's perimeter can be expressed as twice the sum of its length and width.
Given, the length of a rectangle, L = 1 inches
width of a rectangle, W = 6 inches
rate of increasing length, dL/dt = +4 in/sec
rate of decreasing width, dW/dt = -2 in/sec
Now, the perimeter of a rectangle is given by
P = 2L + 2W
Then, the rate of change of the perimeter is
dP/dt = 2 * ( dL/dt) + 2*(dW/dt )
= 2*(+4) + 2*(-2)
= 8-4
= 4 in/sec
Hence, the rate of change of the perimeter is 4 in/sec.
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