Question

A square is getting larger. The sides are each growing at a constant rate of 3 in min . At what rate is the area of the square growing the moment its area is 25 in2

Answer 1

Answer:
`30\ in.^2/min`

Explanation:

Given

The side of a square is increasing at the rate of
`(dl)/(dt)=3\ in./min`

The area of the square is the square of the side length

`A=l^2`

when the area is
`25\ in.^2`, its side must be
`5\ in.`

Differentiate area w.r.t time

`\Rightarrow (dA)/(dt)=2l(dl)/(dt)\\\\\text{Insert the value}\\\Rightarrow (dA)/(dt)=2* 5* 3\\\\\Rightarrow (dA)/(dt)=30\ in.^2/min`