Each side of a square is increasing at a rate of 6 cm/s . At what rate is the ar

Clifton Sanchez

Clifton Sanchez

Answered question

2021-11-22

Each side of a square is increasing at a rate of 6 cm/s . At what rate is the area of the square increasing when the area of the square is 16 cm2 ?

Answer & Explanation

Opeance1951

Opeance1951

Beginner2021-11-23Added 26 answers

Let x represent the square's side length.
Then the area of the square is 
A(x)=x2 
The area of the square is 16cm2 when the side length is x=4 cm 
When x equals 4, we must determine how quickly the area increases.
Differentiate both sides with respect to t. 
dA dt =d(x2) dt  
dA dt =d(x2) dx × dx  dt  
dA dt =2x21× dx  dt  
dA dt =2x× dx  dt  
Given that each side is increasing at the rate of 6 cm/s. Therefore  dx  dt =6 
dA dt =2x× dx  dt  
Given that each side is increasing at the rate of 6 cm/s. Therefore  dx  dt =6 
dA dt =2(4)×(6) 
dA dt =48 
Area is increasing at the rate of 48 cm2s

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