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

b) well because you get well

its an acute right triangle

step-by-step explanation: