Question

The area of a square is increasing at a rate of 2 square feet per minute. How fast is the perimeter changing in feet per minute when the area of the square is 64 square feet?

Answer 1

Step 1)

we know that perimeter of the square with side s is given by,

differentiate both the side with respect to t we can say that,

    --------------------------------------------------1)

Step 2)

we know that the area of the square with side s is given by,

differentiate both the side with respect to t we can say that,

As given area of the square is increasing at a rate of 2 square feet per minute hence we can say that dA/dt = 2

we can write,

    --------------------------------------------------------------2)

we have to find how fast is the perimeter changing in feet per minute when the area of the square is 64 square feet

we will find the side s when area is 64 square feet

we have,

Hence when A = 64 we have,

length of the square can not be negative hence,

Put s = 8 in equation 2) we have,

Step 3)

we have,

Put ds/dt = 1/8 we have,

Hence we can say that when area is 64 square feet perimeter is changing at a rate of 1/2 = 0.5 feet per minute