36 cm²s⁻¹ is the rate at which the area of the square is increasing.
Given each side of the square is increasing at a rate of 6cm/s
Area, A = s², s is the side length
=> [tex]\frac{dA}{dt} =\frac{dA}{ds}* \frac{ds}{dt} =2s*(\frac{ds}{dt} )[/tex] {chain rule of differentiation}
[tex]\frac{ds}{dt}[/tex] = 6 cm/s
When A = 9 cm² => 9 = s²
=> s = √(9) => s = 3 cm
Hence, [tex]\frac{dA}{dt}[/tex] = 2 × 3 × 6 = 36 cm²s⁻¹
Hence, 36 cm²s⁻¹ is the rate at which the area of the square increases
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