Answer:
the rate of change of the area is Ra= 80 mm² per second
Step-by-step explanation:
the area of a rectangle (A) is
A = L * W , L= length and W= width
if the width remains constant the change in the area is only due to the change in length , thus:
ΔA = Δ( L * W ) = W * ΔL , where ΔA represents the change in area and ΔL represents the change in length
ΔA = W ΔL
denoting Δt as the time required to change, and dividing both sides by Δt
ΔA/Δt = W ΔL/Δt
where Ra=ΔA/Δt = rate of change of the area and RL=ΔL/Δt rate of change of the length.
thus
Ra = W * RL
replacing values
Ra = W * RL = 8 mm * 10 mm/second = 80 mm² /second
