The length, l, of a rectangle is decreasing at the rate of 2cm/sec, while the width, w, is increasing at the rate of 2 cm/sec. when l = 12 cm and w = 5 cm, find the rates of change of :
a) the area
b) the perimeter
c) the lengths of the diagonals of the rectangle

A) 14 cm² per sec

B) 0 cm per sec

C) -28 cm per sec

Step-by-step explanation:

We know that,

If l = length of a rectangle and w = width of the rectangle

A) Area of a rectangle,

Differentiating with respect to t ( time )

We have,

B) Perimeter of the rectangle,

Differentiating with respect to t ( time ),

C) Length of the diagonal,

Differentiating with respect to t ( time ),

Since, if l = 12 cm, w = 5 cm,

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