Q. 74.4( 58 Votes )

# The length x of a

Answer :

(a) It is given that the length (x) is decreasing at the rate of 5 cm/minute and the width (y) is increasing at the rate of 4 cm/minute, then we have,

The perimeter (P) of a rectangle is given by:

P = 2( x + y )

= 2(-5 +4) = -2 cm/min

Therefore, the rate of change of the perimeter is -2cm/min.

(b) It is given that the length (x) is decreasing at the rate of 5 cm/minute and the width (y) is increasing at the rate of 4 cm/minute, then we have,

Now, the area (A) of the rectangle is given by

A = x × y

= -5y + 4x

So, when x = 8cm and y = 6cm, then,

Therefore, the rate of change of the area of the rectangle is 2cm^{2}/min.

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