Let sides of rectangular sheet be 8x and 15x where (x is fixed because perimeter of rectangular sheet is constant.)

Now,     V(t) = (8x – 2t) (15x – 2t) t = (4t³ – 46xt² + 120x²t)

V ' (t) = 12t² – 92xt + 120x²

V ' (t) = 0

 $\Rightarrow$        3t² – 23xt + 30x² = 0

 $\Rightarrow$         (3t – 5x) (t – 6x) = 0

 $\therefore \frac{\mathrm{t}}{\mathrm{x}}=\frac{5}{3}$  or   t = 6x (reject)

 $\Rightarrow \mathrm{t}=\frac{5}{3}\mathrm{x}$

Now, 4t² = 100    $\Rightarrow$         t² = 25    $\Rightarrow$         t = 5       $\Rightarrow$         x = 3   

 $\therefore$         sides   are 8x = 8 × 3 = 24

            and       15x = 15 × 3 = 45