Consider a rectangle of length l inches and width w inches. find a formula for the perimeter of the rectangle. use upper case letters. p = l+l+w+w (b) if the length and width of the rectangle are changing with respect to time, find dp dt . use dl dt and dw dt and not l ' and w ' . dp dt = 2( dl dt)+2( dw dt) (c) suppose the length is increasing at 2 inches per hour and the width is decreasing at 3 inches per hour. how fast is the perimeter of the rectangle changing when the length is 40 inches and the width is 104 inches?

a) P=2(L+W)

b)

c)-2 inch/hour

Step-by-step explanation:

given:

length of the rectangle as L inches

width of the rectangle as W inches

a) The perimeter is defined as the measure of the exterior boundaries

therefore, for the rectangle the perimeter 'P' will be

P= length of AB+BC+CD+DA    (A,B,C and D are marked on the figure attached)

Now from figure

    P= L+W+L+W

           OR

=> P=2L+2W        .....................(1)

b)now dp/dt can be found as by differentiating the equation (1)

.............(2)

c)Now it is given for the part c of the question that

L=40 inches

W=104 inches

dL/dt=2 inches/hour

dW/dt= -3 inches/hour    (here the negative sign depicts the decrease in the dimension)

substituting the above values in the equation (2) we get

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