Question

The side length of a square is increasing at a rate of 15 millimeters per second. At a certain instant, the side length is 22 millimeters.

What is the rate of change of the area of the square at that instant (in square millimeters per second)?

Answer 1

`(dA)/(dt)=660 millimetre/sec`

Explanation:

From the question we are told that

Increase rate
`\triangle L=15 millimetre\ per\ second`

Length L=millimetre

Generally the area of the square is given by
`A=L^2`

Therefore

`(dA)/(dt)=\alpha S*(dS)/(dt)`

`(dA)/(dt)=2*22*(15)`

Generally rate of change of area is given as

`(dA)/(dt)=660 millimetre/sec`