A rectangle has a length that is increasing at a rate of 10 mm per second with the width being held constant. What is the rate of change of the area of the rectangle if the width is 8 mm?

Accepted Solution

Answer:the rate of change of the area is Ra= 80 mm² per secondStep-by-step explanation:the area of a rectangle (A) isA = L * W , L= length and W= widthif 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 lengthΔA = W ΔLdenoting Δt as the time required to change, and dividing both sides by ΔtΔA/Δt = W ΔL/Δtwhere Ra=ΔA/Δt = rate of change of the area and RL=ΔL/Δt rate of change of the length.thusRa = W * RL replacing valuesRa = W * RL = 8 mm * 10 mm/second = 80 mm² /second