Answer:
0.67 cm/s
Step-by-step explanation:
The area of a square is given by :
[tex]A=x^2[/tex] ....(1)
Where
x is the side of a square
[tex]\dfrac{dA}{dt}=12\ cm^2/s[/tex]
Differentiating equation (1) wrt t.
[tex]\dfrac{dA}{dt}=2x\times \dfrac{dx}{dt}[/tex]
When A = 81cm², the side of the square, x = 9 cm
Put all the values,
[tex]12=2\times 9\times \dfrac{dx}{dt}\\\\\dfrac{dx}{dt}=\dfrac{2}{3}\\\\\dfrac{dx}{dt}=0.67\ cm/s[/tex]
So, the length of the side of a square is changing at the rate of 0.67 cm/s.
