The length and breadth of a rectangle are x t | vedclass

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Question

(A) Let $x$ be the length and $y$ be the breadth of the rectangle. Given $\frac{dx}{dt} = -5 	ext{ cm/min}$ and $\frac{dy}{dt} = 3 	ext{ cm/min}$.Pe

Vedclass · Accepted Answer

$-4 	ext{ cm/min}$ and $5 	ext{ cm}^2	ext{/min}$

Vedclass · Answer

(A) Let $x$ be the length and $y$ be the breadth of the rectangle. Given $\frac{dx}{dt} = -5 	ext{ cm/min}$ and $\frac{dy}{dt} = 3 	ext{ cm/min}$.Perimeter $P = 2(x + y)$.The rate of change of perimeter is $\frac{dP}{dt} = 2(\frac{dx}{dt} + \frac{dy}{dt}) = 2(-5 + 3) = 2(-2) = -4 	ext{ cm/min}$.Area $A = xy$.The rate of change of area is $\frac{dA}{dt} = x \frac{dy}{dt} + y \frac{dx}{dt}$.Substituting the values $x = 5$,$y = 2$,$\frac{dx}{dt} = -5$,and $\frac{dy}{dt} = 3$:$\frac{dA}{dt} = (5)(3) + (2)(-5) = 15 - 10 = 5 	ext{ cm}^2	ext{/min}$.Thus,the rates of change are $-4 	ext{ cm/min}$ and $5 	ext{ cm}^2	ext{/min}$.

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