Question

A hypothetical square shrinks so that the length of its diagonals are changing at a rate of −8 m/min. At what rate is the area of the square changing when the diagonals are 5 m each?

Answer 1

`-40 m^2 "/ min"`

Explanation:

A square of diagonal `l` has area `A = l/(sqrt 2) * l/(sqrt 2) = l^2/2`

Thus `dot A = l dot l`

here

`dot A = 5*(-8) = -40 m^2 "/ min"`