Question

The width of a rectangle is 8 inches and remains constant, while the length of the rectangle increases at a constant rate of 3 inches per minute. When the length of the rectangle is 6 inches, what is the rate of change, in inches per minute, of the length of a diagonal in the rectangle?

Answer 1

Check the picture below

thus 

$\bf r^2=x^2+y^2\impliedby \textit{now, "y" is a constant, thus }\implies r^2=x^2+64 \\\\\\ 2r\cfrac{dr}{dt}=2x\cfrac{dx}{dt}+0\implies \cfrac{dr}{dt}=\cfrac{x\frac{dx}{dt}}{r}\quad \begin{cases} x=6\\ \frac{dx}{dt}=3\\ r=\sqrt{x^2+y^2}\\ \qquad \sqrt{6^2+64}\\ \qquad 10 \end{cases} \\\\\\ \cfrac{dr}{dt}=\cfrac{6\cdot 3}{10}$