Question

the length of a rectangle is increasing at a rate of 3 cm/hr and its width is increasing at a rate of 2 cm/hr. when the length is 11cm and the width is 18cm, how fast is the area of the rectangle increasing? provide your answer below:

Explanation:

Step1: Recall the area formula

The area of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width.

Step2: Differentiate with respect to time

Using the product - rule $\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}$.

Step3: Substitute the given values

We are given that $l = 11$ cm, $w = 18$ cm, $\frac{dl}{dt}=3\frac{cm}{hr}$, and $\frac{dw}{dt}=2\frac{cm}{hr}$.
Substituting these values into the formula $\frac{dA}{dt}=(11\times2)+(18\times3)$.

Step4: Calculate the result

$\frac{dA}{dt}=22 + 54=76\frac{cm^{2}}{hr}$.

Answer:

$76\frac{cm^{2}}{hr}$