Answer :
The rate of change of the area of the square when the side length is 7cm is 112 .
In the question ,
it is given that
the decreasing rate of the side length of the square is 8 cm per second ,
let the side length of the square be = "[tex]s[/tex]" .
So , ds/dt = -8 cm/s
the formula for area of [tex]s[/tex]quare is ,
area = side²
A = s²
On differentiating both sides with respect to [tex]t[/tex] ,
we get
dA/dt = 2s*ds/dt
Since we have to find rate of change of area when the side length is 7 cm ,
we substitute s = 7 , and ds/dt is given as -8 cm/s
On substitution of values , we get
dA/dt = 2(7)*(-8)
= 14*(-8)
= -112
the negative sign in the answer means that the area is decreasing .
Therefore , The rate of change of the area of the square when the side length is 7cm is 112 .
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