Question

Assume the dimensions of a rectangle are
continuously changing in a way so that the area, A, of the rectangle
remains constant. If the base of the rectangle is increasing at a rate
of 3 inches per second, at what rate is the height of the rectangle
changing at the instant when the rectangle is actually a square? Is
the height increasing or decreasing at this instant? Include units.
Show all work.

Answer 1

let the base be x
let the height be y
then
A = xy
dA/dt = x dy/dt + y dx/dt
but dA/dt = 0

x dy/dt = -y dx/dt
given:
dx/dt = 3,
find : dy/dt when x = y

x dy/xt = -x(3)
dy/dt = -3

So at the moment when it turns into a square, the height is decreasing at 3 inches/second

Answer 2

Thanks!