Question

A square plate is contracting at the uniform rate of 3cm²/sec. The rate at which the perimeter is decreasing when the side of the square is 12 cm long is

Options

• `1/2`cm/sec

• `1/3`cm/sec

• `1/4`cm/sec

• none of these

Answer 1

`1/2`cm/sec

Explanation:

Let A, P and x be the area, perimeter and length of the side of the square respectively at time t seconds. Then, A = x² and P = 4x

∴ P = `4sqrt"A"`

∴ `"dP"/"dt" = 4 * 1/(2sqrt"A") * "dA"/"dt"`

`= 2/x * "dA"/"dt" = 2/12 * 3 = 1/2` cm/sec