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?

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