Mathematics

Problem

The area of a square metal sheet is increasing at the steady rate of

96\,\text{cm}^{2}\!\!\text{/s}

. Let

x\,(\text{cm})

denote the length of a side and

d

the length of its diagonal at time

t\,(\text{s})

. (i) Find the rate of change of

x

when the area of the square is

144\,\text{cm}^{2}

. (ii) Hence determine the rate of change of the diagonal

d

at the same instant.