Answer:
-39 cm²/h
Step-by-step explanation:
The area of the rectangle is A = hw where h = height and w = width.
So the rate of change of area with respect to time is
dA/dt = d(hw)/dt
dA/dt = hdw/dt + wdh/dt
Given that at an instant h = 3cm, w = 8 cm and dh/dt = + 11 cm/h and dw/dt = -9 cm/h(negative since it is decreasing)
So, dA/dt = hdw/dt + wdh/dt
dA/dt = 3 cm × (+11 cm/h) + 8 cm × (-9 cm/h)
dA/dt = 33 cm²/h - 72 cm²/h
dA/dt = -39 cm²/h
