The side of a square sheet is increasing at the rate of 4cm per minute. At what rate is the area increasing when the side is 8 cm long?

Explanation

Given :

`A=x^{2} and frac{d x}{d t}=4` cm / min

Let x be the side of the square and A be its area at any time t.Then,
`

A=x^{2} `
`
Rightarrow frac{d A}{d t}=2 x frac{d x}{d t} `
`
Rightarrow frac{d A}{d t}=2 times 8 times 4(because x=8 {cm} text { and } frac{d x}{d t}=4 `cm / min))

`Rightarrow frac{d A}{d t}=64 {cm^{2}} / min`