Answer to Question #319963 in Calculus for ion

Question

if the base X of the right triangle shown is increasing at the rate of 3 inches per second and the height Y is decreasing at the rate of 2 inches per second, find the rate of change of the area of the triangle when X = 5 inches and Y = 7 inches. Label the units on your answer

Answer 1

$S=\frac{1}{2}XY\\\frac{dS}{dt}=\frac{1}{2}X\frac{dY}{dt}+\frac{1}{2}Y\frac{dX}{dt}=\frac{1}{2}\cdot 5\cdot \left( -2 \right) +\frac{1}{2}\cdot 7\cdot 3=5.5\\The\,\,area\,\,increases\,\,at\,\,a\,\,rate\,\,5.5 inches/\sec ond$