Question

At a given instant, the legs of a right angled triangle are $8\text{cm}$ and $6\text{cm}.$ If the first leg decreases at the rate of $1\text{cm}/\text{sec}$ and the second leg increases at the rate of $2\text{cm}/\text{sec}$ respectively, then the rate of change in the area after $2sec$ is equal to $\left({\text{in cm}}^2/\text{sec}\right)$

• A. 1
• B. 1.0
• C. 1.00

Answer 1

Answer: (A), (B), (C)

$\text{Let,}x=8\text{cm},y=6\text{cm}\text{(at a given instant)}$
$\text{Given},\frac{dx}{dt}=-1\text{cm}/\text{sec}\frac{dy}{dt}=2\text{cm}/\text{sec}$
$\therefore \text{After}2\text{sec},x=6\text{cm},y=10\text{cm}$
$\text{Area of triangle,}A=\frac{1}{2}xy\Rightarrow \frac{dA}{dt}=\frac{1}{2}(x\frac{dy}{dt}+y\frac{dx}{dt})=\frac{1}{2}\left(\right(6\times 2)+(10\times (-1)\left)\right)=1{\text{cm}}^2/\text{sec}$