# The length of a rectangle is decreasing at the rate of 5 cm/min. and the width y is increasing at the rate of 4 cm/min.

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The length of a rectangle is decreasing at the rate of 5 cm/min. and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the change of (a) the perimeter (b) area of the rectangle.

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Given,

$\frac{dx}{dt}$ = - 5 cm/min,

$\frac{dx}{dt}$ = 4 cm/min

Let x = length, and y = breadth

Perimeter of rectangle P = 2 (x + y)

∴ Rate of change of P is

∴ Perimeter is decreasing at  2 m/s

If A be the area of rectangle then,

A = x . y

Differentiating w.r.t. 't', we get