Question

SCALCET8 3.9.003. Each side of a square is increasing at a rate of 4 cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm2

Answer 1

24cm^2/ s

Explanation:

Answer 2

Answer:
`24\ cm^2/s`

Explanation:

Given

Each side of square is increasing at a rate of 4 cm/s

Side of a square when area is
`9\ cm^2`

Suppose a is side of the square

`\Rightarrow a=√(9)\\\Rightarrow a=3\ cm`

Area is given by

`\Rightarrow A=a^2\\\text{Differentiate area w.r.t time}\\\\\Rightarrow (dA)/(dt)=2a(da)/(dt)\\\\\Rightarrow (dA)/(dt)=2* 3* 4\\\\\Rightarrow (dA)/(dt)=24\ cm^2/s`

Area is increasing at a rate of
`24\ cm^2/s`