Question

The area of the square increases at the rate of 0.5 cm²/sec. The rate at which its perimeter is increasing when the side of the square is 10 cm long is ______.

Options

• 0.2 cm/sec

• 0.3 cm/sec

• 0.4 cm/sec

• 0.1 cm/sec

Answer 1

The area of the square increases at the rate of 0.5 cm²/sec. The rate at which its perimeter is increasing when the side of the square is 10 cm long is 0.1 cm/sec.

Explanation:

We have,

Area of the square increases at the rate of 0.5 cm²/sec.

`therefore "dA"/"dt" = 0.5 "cm"^2//"sec"`

A = x²

`=> "dA"/"dt" = 2x "dx"/"dt"`

Perimeter of square, P = 4x

`"dP"/"dt" = 4 "dx"/"dt"`

`"dP"/"dt" = 4/"2x" "dA"/"dt"`

`= 4/*(2 xx 10) xx 0.5`

= 0.1 cm/sec