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Lelu [443]
2 years ago
11

Each side of a square is increasing at a rate of 2 cm/s. at what rate is the area of the square increasing when the area of the

square is 9 cm2?
Mathematics
1 answer:
faltersainse [42]2 years ago
3 0
Let x(t) =  the length of a side of the square (cm) at time t (s).
The rate of change of x is given as
\frac{dx}{dt} =2 \,  \frac{cm}{s}

The area (cm²) at time t is 
A = x²

The rate of change of the area with respect to time is
\frac{dA}{dt} = \frac{dA}{dx}  \frac{dx}{dt} =2 \frac{dA}{dx} =2(2x)=4x \,  \frac{cm^{2}}{s}

When A = 9 cm², then x = √9 = 3cm. Hence obtain
\frac{dA}{dt} = 4(3) = 12 \,  \frac{cm^{2}}{s}

Answer: 12 cm²/s

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